The problem with this question is that it's a lot more complicated than it looks on the surface, because you're basically asking, "What qualifications do Presidents use to decide upon a Supreme Court nominee?" There have been all sorts of law review and history articles written on this - including this megathread after Justice Scalia's death by /u/Georgy_K_Zhukov, and there's no real consensus besides that the nominee needs to be someone who is 1) an attorney that someone who is close to the President is aware of (or often until early in the 20th century, the President knew himself) and 2) someone the President thinks can survive the confirmation process.

Beyond that it has substantially varied by circumstances. LBJ wanted his personal attorney Abe Fortas nearby in Washington for routine consultation and brutally wore him down to drop his long-stated opposition to taking the massive pay cut that a Court seat would entail. This worked for a few years, but ended up backfiring tremendously once Fortas decided he needed to supplement his income to maintain his lifestyle when he took a fairly lucrative side job that demanded almost no work running a foundation for someone convicted of securities fraud, which became the nominal reason he was forced to resign from the Court in 1968. A half century earlier, Wilson appointed Louis Brandeis largely because the two men had mutually impressed each other with their commitment to Progressive reforms. Between earning plentiful enemies for these politics along with anti-Semitism, Brandeis spent four months in committee during a time when nominees usually didn't bother even testifying and were confirmed in an afternoon. However, both of these examples wouldn't fit your thesis; Yale Law grad Fortas was generally regarded as one of the best attorneys in the country and founded what's now the white shoe megafirm Arnold & Porter, and Brandeis graduated with the highest GPA in the history of Harvard Law.

Politics play a significant factor as well, with Eisenhower providing a good example. His first appointment, Earl Warren, was promised the first opening on the Court (Ike tried to renege, but Warren insisted) in exchange for dropping out of the Presidential race in 1952 and swinging the California delegation. His third, William Brennan, was mostly in the right place at the right time. From Stern and Wermiel's Justice Brennan:

Eisenhower wanted a nominee with experience on lower courts, whether at the federal or particularly the state level. The Conference of Chief Justices of State Courts had pressed Eisenhower to consider the latter, since no state judge had been appointed to the Court in twenty-seven years. Eisenhower was clear that his nominee should be relatively young and healthy. And he wanted, if at all possible, the nominee to be Catholic...no Catholic had served on the Court since Justice Frank Murphy, appointed by Roosevelt, died in 1949, ending fifty-five years of consecutive service by a Catholic, and [political kingmaker] Francis Cardinal Spellman argued that Eisenhower should appoint a Catholic not just for the sake of maintaining a "Catholic seat." Instead, he emphasized the many issues involving the Catholic Church facing the Court...

In addition, Eisenhower was two months away from the 1956 presidential election - which he felt was a lot closer at the time than the results ended up turning out - and the Catholic vote mattered. He asked his Attorney General, Herbert Brownell, for a candidate that was "a very good Catholic, even a conservative Democrat." Brownell and Deputy AG William Rogers met and screened for potential candidates that met Ike's criteria (the "young and healthy" was interpreted to be someone under 62, since there'd been a number of prominent people dropping over dead in a short time and Ike didn't want to inadvertently backdoor his own heart condition into a campaign issue), and on the federal bench and state appellate levels there were a grand total of 3 men who fit them. One was Brennan, who conveniently had worked with both men on a committee - and voila. Brennan was tapped for the job, became probably the most influential justice of the 20th century, and his Harvard Law degree played almost no role.

So it's generally hard to quantify precisely why nominees were picked in the first place unless you look at them on an individual basis. But since you ask about post-1969, it does lead to one of my favorite stories about the Court - which may indeed play a role in why the academic qualifications of nominees seem to be more scrutinized now than in the past.

Following Fortas' resignation, Nixon attempted to push through a couple of far more conservative nominees. Clement Haynsworth was probably reasonably well qualified but had issued rulings that supported segregation and union busting, and between that and other reasons became the first nominee to be rejected by the Senate since the NAACP and Progressives had organized to defeat Hoover nominee John Parker in 1930.

Then came Harrold Carswell, who had made controversial statements on segregation and who even supporters suggested was not exactly a shining light of jurisprudence. From Farganis and Wedeking's Supreme Court Confirmation Hearings in the U.S. Senate: Reconsidering the Charade:

Even Carswell's defenders in the Senate were lukewarm in their support, often attempting ot recast his "mediocrity" as an asset rather than a liability. For example, Louisiana senator Russell Long said, "Does it not seem that we have had enough of those upside down, corkscrew thinkers? Would it not appear that it might be well to take a B student or a C student who was able to think straight, compared to one of those A students who are capable of the kind of thinking that winds up getting a 100% increase in crime in this country? Senator Roman Hruska added "There are a lot of mediocre judges and people and lawyers, they are entitled to a little representation aren't they? We can't have all Brandeises, Frankfurters, and Cardozos!"

Unsurprisingly, even with Nixon spending a significant amount of political capital on the nomination, Carswell was rejected 51-45, and Nixon finally caved in and appointed more moderate (and double Harvard degree holder) Harry Blackmun. However, given the general negative consensus about Carswell's credentials, this may very well be why no President since then has tried to nominate anyone who might have a whisper of controversy regarding their academic qualifications.