>The U.S. tends towards a “trust but verify”

The impression I get is the US tends towards a "protect the lobby income streams" approach. Specifically related to taxes: the IRS has the majority of the information it needs to just send you a tax bill/credit. And cases where they don't can be rectified by submitting that information which isn't (like rental income, which AFAIK you are supposed to be reporting and paying quarterly taxes on anyway).

The reason they don't seems to largely be that the tax prep industry has lobbied to keep it from happening, and shut down "free file" by the IRS.

I think you might be misunderstanding that phrase.

Quizzically, the old Russian proverb “trust but verify” is not the experience I expect from US governments, but rather “punish if caught”.