As I'm sure you can see from the number of deleted comments, whether moderator-removed or user-removed, this question is difficult to answer without becoming overtly political. I will do my best to maintain neutral, but I encourage you to cross-post this question in r/Ask_Politics for a look at some of the political history behind the current US healthcare system.
First, it is notable that the history of nationalized healthcare worldwide is a complex tapestry, with different nations adding different rules at different times. National Health Insurance can be implemented in many different ways--for example in Canada hospitals and doctors are private, but the government pays for health insurance through the usage of taxes. Contrast this with the United Kingdom's NHS, where the hospitals are nearly all publicly owned (there's a small number of private health providers, but the vast majority of people are served by public doctors), or Germany, where health insurance is mandatory, most people are government-enrolled into a small number of insurance providers, but some others purchase private insurance. All of these cases are considered "nationalized health care" compared to the United States. Furthermore, contrary to the implicit assumption of the question, not all developed countries added nationalized health care systems directly following WW2. For example, Canada only expanded its national health insurance plan to all provinces in 1972 after tremendous doctors' strikes, whereas the UK implemented the NHS in 1948. I'd argue that these are sufficiently different political moments that characterizing them as both "post-WW2" oversimplifies the situation significantly.
To fully answer your question would take several books. If you're particularly interested in this topic I urge you to check out the following books, that I'll be summarizing liberally:
Jill Quadango: One Nation Uninsured: Why the U.S. Has No National Health Insurance
John Burnham: Health Care in America: A History
John E Murray: Origins of American Health Insurance: A History of Industrial Sickness Funds
Paul Starr: The Social Transformation of American Medicine: The Rise of a Sovereign Profession and the Making of a Vast Industry
Quadango and Starr are sociologists, Murray is a political economist, and Burnham is a historian.
Other Sources I cite:
Lee Igel: The History of Health Care as a Campaign Issue
Edwin Witte: Reflections On The Beginnings Of Social Security
Peter Corning: The Evolution of Medicare. . . from idea to law
First I'm going to endeavor to answer your question on its most literal level: for what reasons did 20th century US attempts to establish a national health system fail? Multiple attempts were taken throughout the 20th century with the goal of establishing some form of National Health Insurance. National Health Insurance was a campaign issue in 1912, with healthcare advocates supporting Theodore Roosevelt (running on the Progressive Party Ticket) for president. It's not entirely clear what exact healthcare system would have resulted from a hypothetical Roosevelt win, but the question is rendered moot as instead Woodrow Wilson became president. Iger argues that while Wilson (whose legacy is incredibly complicated) acted on some progressive priorities, healthcare was sidelined because of the impending World War I. Instead, the task of passing National Health Insurance would pass to Theodore's cousin, Franklin Roosevelt. Edwin Witte, the head of FDR's Committee on Economic Security, considered including health reform in the Social Security Act. I quote at length from a speech he gave in 1955, on the 20th anniversary of the Social Security Act (emphasis mine):
Health insurance was little discussed by most of the members of the staff or by the Technical Board and was given no consideration in Congress, but was intensely studied by the health insurance staff of the Committee and received a good deal of attention at top Committee levels and at the White House****. Originally, it was expected that the Committee would have to deal with this subject in its recommendations, but by the time that its Report had to go to the President, the staff and the Medical Advisory Committee had nothing to offer. So the Report merely stated that the Committee on Economic Security would make a later report on the subject**,** and the Administration bill merely provided for Federal aid for public health services, with a provision that the Social Security Board should study the need for and possibility of improving the social security protection of Americans, including, among others, health insurance. This innocent reference to health insurance led to the first special Meeting of the House of Delegates of the American Medical Association, in the false belief that the Administration was secretly trying to foist compulsory health insurance on the country**. Immediately,** the members of the Ways and Means Committee, then considering the social security bill in executive sessions, were deluged with telegrams from all parts of the country protesting against this "nefarious plot." The upshot was that the Committee unanimously struck out the specific reference to study of health insurance to which A.M.A. officials objected. Later, at a time when there was serious doubt whether any social security legislation at all would be enacted, the health insurance staff presented a report recommending Federal aid to States which might establish a health insurance plan, which the Committee on Economic Security endorsed. The President deemed it inadvisable to proceed along that line and the report was never even published. The attention given by the Committee to health insurance probably was a factor, however, in the reversal of its prior position of opposition to voluntary forms of health insurance which the A.M.A. executed at the Special Meeting of the House of Delegates in February 1935. The launching of Federal aid to the States for public health services, provided for the Social Security Act, was a most important step toward more extended and improved public health and medical care services, which has been such a marked trend in the last 20 years. The inclusion of these provisions brought valuable support to the Social Security bill in Congress, as did also the aids for child health and welfare services, for which Miss Grace Abbott, Miss Lenroot and Dr. Eliot, all connected with the Children's Bureau, and Miss Perkins, were mainly responsible.
Witte, one of the chief architects of the New Deal, places the blame for the failed healthcare reform attempt squarely on the shoulders of the American Medical Association, an industry trade group who he claims torpedoed the bill by lobbying against it. It is notable that 1. This source, like all sources, has a bias 2. This healthcare reform would be more like the ACA (compulsory health insurance) than true nationalized health insurance. In any event, healthcare reform was not passed in the first wave of New Deal Legislation.
The next wave of attempted reform fits nicely in the post WWII moment you pinpoint in your question. 1n 1943, the Wagner-Murray-Dingell bill was proposed (not to be confused with the Wagner act, which regulated private sector collective bargaining rights). Organized labor and farmers’ groups lobbied in favor of the bill, while Physicians and Insurance Trade groups lobbied against. The bill died in committee in 1943, and while healthcare was included in FDR’s proposed Economic Bill of Rights, the issue was postponed.
On FDR’s death, Truman took up the challenge of National Health Insurance, sending a revised Wagner-Murray-Dingell bill to congress in 1945. At the time of the bill’s introduction, 74% of Americans were in favor, per Corning. This is probably the closest National Health Insurance ever came to passing, but a set of circumstances combined to ensure its failure. First, the structure of the US congress at the time was such that progressive legislation was unlikely. Congress operated on a rigid seniority system, which gave conservative Southern Democrats more powerful committee chair positions. The power of the committees at the time was greater than in the current political system, so lacking the support of a chair could be a death sentence for a bill. The Chair of the Ways and Means Committee at the time was Robert Doughton, a Democrat from North Carolina, was relatively moderate (his first dimension DW-Nominate score shifts from -.3 to 0.1 while he served) and opposed the bill. Second, gerrymandering (according to Corning, who I rely on heavily for this bit) resulted in rural areas being overrepresented, thus enabling conservatives to block the bill. Third, congress became bogged down debating between differing proposals on how exactly to implement a national insurance system. Fourth, and perhaps most importantly, the immediately post WW2 era happened to be one of extraordinarily weak political parties. Strong political parties demand party unity on controversial issues, but disunity amongst Democrats and Republicans hampered progress on an bill that could be passed. In 1946, in part due to backlash from healthcare attempts, Republicans won the house for the first time in a decade and a half, de facto ending negotiations. With the advent of the cold war, and a minor recession in 1948, healthcare reform was tabled for a later date. When it was picked up again 20 years later, it was in the form of Medicare proposed by Kennedy and Johnson, scaling back on the ambitions of the prior administrations. The fight for Medicare is a fascinating one, but it is not a true National Health Insurance program. By the time Medicare was proposed, nationalized health insurance had taken on a patina of socialism fatal to any bill’s prospects.
In the short run, America’s political system moved relatively slowly, special interest groups were actively opposing national health insurance, national security concerns and untimely political events distracted from health care, and it kept getting postponed until a point at which it became politically toxic. This mostly only covers the short-term causes of some of the reasons that specific national health insurance attempts failed—I’ll look at some comparative politics reasons tomorrow, but I thought this might be enough to give people something to jump off of/think of follow up questions.