Since 1958 with the Former Presidents Act [1] the Presidency guarantees you'll live very comfortably for the rest of your life with a lifetime pension (and even a small pension for your wife), funding for an office/staff, lifetime secret service protection, funded travel, and more. It was passed precisely because of the scenario you describe playing out with Truman who was rather broke, and ran into financial difficulties after leaving office.

[1] - https://en.wikipedia.org/wiki/Former_Presidents_Act

Are most fresh grads from a top PhD program really making $400k/year? Sure, the ones hired by OpenAI are making at least that much, but the vast majority are not. However the broader point remains, that the president’s (and the rest of government’s) pay structure has not kept up with the private sector.