Well, if they'd wanted, in 1936 and 1940 conservatives could have certainly had another go at him given he was a more than eager and willing candidate, but it is equally telling that what public rehabilitation he gained took place after World War II - once the electorally disastrous possibility of him actively running for office had finally faded.

I won't go into detail about Hoover's long and generally successful career prior to his administration save to note that in 1919 and 1920 he was perceived much like Eisenhower was in 1948, which was as someone whose party affiliation and politics were entirely unclear but whose presidential stock was extremely high. Many Progressives felt Hoover was perhaps their best shot at retaining the Presidency, and given he'd been fairly loyal to Wilson (and saved hundreds of thousands of lives running food relief to Europe), their conclusion was that he was a potential Progressive Democrat - including FDR, who tried to recruit him.

But Hoover wasn't interested; underneath, his beliefs, politics, and affiliation were rather different. I bring his early political history in, though, to explain one reason (besides the obvious one of his later electoral toxicity) as to why conservatives tended to embrace rather than adore Hoover despite his record as a Cabinet member of the 1920s as well as his advocacy following his administration.

That administration, as you note, is indeed still generally considered a disaster despite some revisionism in recent years. But this AMA with Eric Rauchway really points out the basic reason why some conservatives even back then discounted those four years: that Hoover and his policies remained the polar opposite to the New Deal. Regardless of how bad things were during his Presidency - and they were terrible, especially in the horrid winter that Rauchway's book covers where even William Randolph Hearst solidly lines up behind FDR - his administration offered a what-might-have-been glorious conservative standard versus the horrors of the New Deal. Moreover, the finger pointing began very shortly thereafter in terms of how much of the early New Deal came from implementing and expanding initiatives that the Hoover administration had come up with on their own, so an alternative narrative for conservatives took root early on.

I won't be addressing New Deal and Hoover policy questions in this thread - those are a top-level worthy and extremely complicated set of separate issues - but I bring it up to explain why even during the depths of the Great Depression as to why Hoover's reputation among die hard conservatives was never anywhere close to the dismal one he had among voters overall. In turn, Hoover became the single most strident advocate against the New Deal, which as Kenneth Whyte points out:

"In Hoover’s judgment, the New Deal’s scale, reach, and coercive nature were so far beyond anything America had known as to represent a new and dangerous doctrine in national political life."

Hoover goes so far as to write a book a decrying it - thanks to a deal with the Book of the Month club, it sells 100,000 copies - then watches in shock in 1934 as he's further repudiated in the midterms. But even sympathetic Republicans know he is now a political liability even if he's still trying to be a standard bearer:

"(When an) old friend...advised not speaking against the New Deal until FDR’s popularity had abated, Hoover suspected him of sordid motives...(but with the friend's) wide acquaintance(s) in Republican circles, he understood that the party was eager to turn the page and forget about its Depression president. It wished Hoover would pipe down. Three (conservative) journalists...transmitted similar messages to (Hoover's circle): Hoover, never a true member of the Republican guild, now represented its greatest disaster, and it was time he step aside for new leadership."

Despite this, Hoover tries to run for the nomination in 1936 without campaigning, notwithstanding polls presented to him showing his support at 4%; even a highly favorable biographer like Whyte describes Hoover's political aspirations at this point as "delusional." He lobbies non-stop, makes a prime time convention speech to delegates lambasting the New Deal as "quackery...a cold blooded attempt to Europeanize the country" that results in a wild 15 minute demonstration among 18 states, and has hope for a few hours that he might be the nominee. He gets not a single vote, a sign of his political impotence despite his value as the conservative standard bearer.

Unbowed by this, Hoover keeps thinking he's got a shot - this time with the unpopular court packing plan, which threatens the Supreme Court majority that continues to block large parts of the New Deal. He goes on the speaking circuit, eviscerating the New Deal and FDR, which now finally gets some traction. The 1937-1938 recession provides him with a little more, and Hoover - who has always avoided political labels - finally outright identifies himself as a 'conservative', mostly against the 'liberalism' that FDR represents.

He continues on the speaking circuit, and despite the immense baggage some party members think he might have an outside shot going into 1940, since there's a 4 way split going in to the convention and no candidate has enough commitment to outright win on the first ballot as Landon did in 1936. (Indeed, Wendell Willkie shocks the political establishment by becoming the dark horse nominee on the sixth ballot after one of the great convention uprisings.) Hoover gives what some call the best written speech of his life to try to sway the convention, but there's a problem. The microphone to the hall has issues - Hoover in his paranoia later seeks out someone to swear an affidavit that it was sabotaged - and while the one to the national broadcast more or less works, almost nobody inside can hear what he's saying! So Hoover's last political stand fails, and he spends World War II exiled as FDR wants absolutely nothing to do with him, probably wisely; Hoover is outraged that Lend Lease includes the Soviet Union, since "those two bastards [Hitler and Stalin] [should] annihilate themselves," that the policy towards Japan is poking a rattlesnake with a pin, and that prior to Pearl Harbor getting into the war is part of political calculus by FDR.

Truman brings him back for food relief advice - Hoover at 70 is finally not a candidate in 1944 - and they eventually have a very warm relationship (the last letter Hoover ever writes is to Truman), even though Hoover initially thinks of him someone "really dumb" who could not grasp "the vital points of any issue" and is a "mediocre type of man." Yet, Truman has him in Europe in 1946 and 1947 talking logistics with European countries trying to manage the famine, and he does a fairly decent job of it, rebuilding his wider reputation slightly. That said, Truman campaigns against Hoover in 1948 as much as he does against Dewey, and for a while Hoover is furious at him.

During 1952, while he's still out speaking as he has been for years, Hoover is not actively campaigning - but his views now comprise what is considered to represent the mainstream conservative wing of the Republican party, consisting of people like Robert A. Taft. Unfortunately for both, Eisenhower wins overwhelmingly and is a much more moderate President, even if Hoover makes one last widely seen appearance (at 85!) at the Republican convention in 1960, where he bemoans America's "moral slump" as "an infection from Communist Russia" as well as "beatniks and eggheads" who were destroying national pride.

All this means that by the time you're asking about, Hoover is really seen as the historic godfather of the conservative wing of the Republican party - as well as circa 1971, being the only conservative President of the last 40 years - regardless of how he got there. That is undoubtedly what Archie Bunker's song is referring to, since it's a perception of a personification of the good old days - along with the rather sarcastic overlay of producer Norman Lear pointing out that the fictional Bunker really didn't want to look all that closely at what they entailed because they may not have been all that good.

Sources: Hoover, An Extraordinary Life in Extraordinary Times (Whyte, 2017), Winter War (Rauchway, 2018), Herbert Hoover in the White House (Rappleye, 2016), Dark Horse (Neal, 1984), Man of the People (Hamby, 1995)

There are a few things to unpack here. Historians have begun to reevaluate Hoover's presidency and his management of the early Great Depression era. Generally, we have concluded that he was not entirely dormant or inactive as he was typically portrayed. He did push for intervention in the economy mainly through financial institutions to keep credit and loans flowing in order for big businesses to create jobs and not go under. In hindsight, and a bit ahistorical, Hoover is cast as one of the "worst" presidents when compared to FDR's political choices mainly in the second New Deal and the WWII economic boom. Keep in mind that FDR did not end the depression. It was the wartime economy that generated immense government spending.

Now, let's also note that FDR's first term and first New Deal was also a large failure for working people. FDR, just like Hoover, established mainly financial fixes for the economy: bank loans, credit, and mortgage support. FDR's policies guaranteed the loan market so if one defaulted the bank would not lose money. In this agreement, he also ensured that municipal bonds investments were not taxed and other loans have guaranteed interest rates. These policies incentives banks and financial institutions to invest and keep the economy moving. Hoover and FDR really approached the economy the same way by trying to guarantee that financial institutions would not falter in order for consumer capitalism to function again.

With that quick aside, the Archie Bunker's of the 1970s were most likely reacting to a shift in the political environment. Bunker was a union man, he was invested with working-class politics, and came of age in an era between the 1940s and 1960s when American workers benefited from what historians have called the "New Deal order." Briefly, the New Deal Order was a consensus and agreement between unions, corporations, and the federal government that guaranteed a prosperous post-war period with high union wages, no strikes, and profits. Some workers could afford homes and luxury goods. Because of such successive organizing, we have the political section of the democrat party who called themselves "New Deal Democrats." These New Dealers were poised to continue the tradition that FDR had set and advocated for a Keynesian economy with government regulation.

But here is the biggest flaw of the New Deal: it was very racially exclusive. White workers benefited the most from the post-war New Deal order. African-Americans, women, and other people of color could not have the same access to this post-war world. So what happens in the 1960s? The Civil Rights movement! These folks who were excluded from this post-war economy protest for inclusion or remedies. Lyndon B. Johnson, the last true New Deal democrat, begins to invest in these communities with his Great Society programs. Urban rebellions rock the nation, the war in Vietnam is largely unpopular, and the wartime economy begins to falter. There is so much going on in the late 1960s, too much for this one post.

Here is where Archie Bunker comes in. He was part of a reactionary conservative movement seeing the world around them change and channeling it in terms of race and anti-tax sentiment. He saw the post-war economy start to deindustrialize but to them, it was not factories moving abroad but African Americans and immigrants taking jobs. It was not that the economy was no longer centered on the core industry of the past but poor people becoming a drain on federal and local coffers. The issue was one of culture, not the economy. The New Deal Democrats with their big-spending bills on public housing programs and federal interventions on welfare were to blame. Archie did not want a New Deal Democrat as president anymore. Perhaps, a Herbert Hoover was what the nation needed. A man who was not interested in funding the public but fixing the economy. Bunker and conservatives, to answer your question, missed the political economy style of Hoover. As mentioned above, Hoover was unpopular with his opponents and the ahistorical idea of him being the worst president is just that.

PS: For a great overview on "All in the Family" see Jefferson Cowie's chapters in Sayin' Alive: The 1970s and the Last Days of the Working Class. Cowie offers a great exploration of white working-class popular culture and Archie Bunker is at the top!