I would've given it to Fun Home over The Flick, but maybe the fact that Fun Home was an a adaptation was a bit of a demerit (I realize that adaptations have won before, but I think they prefer to give it to original works)
I agree Company is a good choice. Looks like it lost to No Place to Be Somebody, which was notably the first award to go to a Black playwright, and also the first Off-Broadway play to win. So I guess it's hard to begrudge those significant milestones, though I haven't read or seen the play, personally.
Follies, maybe? I'm not familiar with the play that won that year. ("The Effect of Gamma Rays on Man-in-the-Moon Marigolds"
I know it's not about "american life," and also an adaptation, but I think Fiddler on the Roof should've been in the mix. And that was eligible for 1964? No Pulitzer was even given that year.
The Scottsboro Boys seems like another contender, which interestingly was eligible in the same year as Next to Normal - unless they waited for the Bway run to submit for eligibility, in which case it would've been eligible the following year, when Clybourne Park won. I definitely would've given it to Scottsboro Boys over Clybourne Park, personally.
Also, preemptively: Oratorio For Living Things. I assume it's not going to win for 2022, but I think it should.
Runaways comes to mind - it would've been eligible the year that Gin Game won. I haven't read or seen Gin Game (I skipped the recent revival), so I guess I can't speak to whether it was deserved or not.
And I agree about Caroline or Change- depending on when they submitted, I guess it would've been eligible in either 2003 (Anna and the Tropics) or 2004 (I Am My Own Wife)