isn't there a lot other AXs hand and big pair that's in his range, is there a reason to believe that he'd check 2P+ or c/r bluff at this river? why not bombard it like a missed fd and let him catch us bluff

From his perspective you check/called him twice which says you have a weak made hand or air. He check/calls the river induce a bluff from you and also since he has top top and getting 3 streets of value from top pair would be thin and he wouldn't know how to react to a raise on the river.

Sorry, stupid questions:
Why is it bad to check AK on the river, given that Hero's range contains AK? Is everybody 3betting AK vs UTG nowadays? Seemed a bit different to me 2 months ago when only Russian "I don't know what to do post, so I 3bet"-donks constantly 3bet every 2 cards they liked.

Given that, why is it a fundamental problem to check AK here as villain, given that a) Hero can have 2pr + AK, and b) Villain can have a load of 2Pr/sets, but really not too many draws compared to those 25 combos (according to terp) who should bet river? TBH, given bluff-to-value-ratio there should be GTO bet-size of 1/5 or smth - if you include AK into you value range.

Closely related to these questions: Why does everybody assume ATo is in UTG's range? I know no good TAG up to 28/22 who would open this UTG.
Why is ATo in BTNs calling range? I know no good TAG up to 28/22 who would cold-call an UTG raise with this. Even ATs seems marginal at this point.

You are ignoring case (c) hero has hands we want to valuebet against that may or may not check behind.

If hero does not 3bet AK it's somewhat likely hero does not 3bet QQ either. As villain, we want to valuebet against QQ.
Hero will have a lot of AQ in his range and we want to valuebet against that usually.

Against AK it doesn't really matter if we bet or check.

We can't know how many Axs/AT villain has but your claim
Is really strange. Good TAGs don't have ranges that are set in stone. BB has 50bb, I'd say most good TAGs will notice that and open ATo if the table isn't very aggro etc
Obviously you don't know me and you don't know if I'd qualify as a good TAG but I can give you my word that I snapopen ATo at this table as UTG untill I get a good reason not to.
[My "standard" is to fold even AJo UTG FWIW]

Funny, ATo is really an easy fold to my ppl. Not even a discussion. Unless of course - blahblah - we have only nits behind us, and the fish in the blinds - then, only then, would UTG ATo make sense. Or you are durrr - or CombatCarl with the right sense of timing.
As if 23/21s std UTG range would include ATo.
Don't make it sound more complicated than it is.

??? Hehe, yeah, but I think I know you better than random reg who knows you. Anyway, AJo marginal open IMO. No problem in folding it.

Gonna try to reply tomorrow to the first part. If necessary. Which I doubt. But thanks.

Maybe I didn't get what I tried to say across correctly. ATo is a standard open for me UTG with a 50bb dude in the blinds and no other history.
As a default AJo is a fold for me UTG (i.e. same table but BB has 100bb).

I'm way more concerned with playing as many hands as possible against the fish than worrying about reg-ish players making moves on me/making my life hard.

Alright. That's much more interesting. But IMO wrong.
But tomorrow. Sorry!

Well, one last stupid question to OP: Was there a fish in the blinds? And did 23/21 UTG appear to be fish-LAGgy - as clowntable appears to be?

This is false IMO. You have too much opposition behind you, unless you play like ... 25NL.

Don't know why, but AJo is a profitable open UTG in my book. According to stats.

See CombatCarl opening 97s UTG only to play vs fish. No, it isn't really profitable to play ATC against fish.

What? I won that 97s hand against those two fish. I had both of them killed from start to finish. Do you wanna see the result?

What's wrong with opening ATo on UTG? I do it all the time.

Poker Stars, $1/$2 No Limit Hold'em Cash, 6 Players

BTN: $414.63 (207.3 bb)
SB: $262.65 (131.3 bb)
BB: $446.53 (223.3 bb)
Hero (UTG): $227.68 (113.8 bb)
MP: $416.16 (208.1 bb)
CO: $102 (51 bb)

Preflop: Hero is UTG with T A
Hero raises to $6, 4 folds, BB calls $4

Flop: ($13) T A 6 (2 players)
BB checks, Hero bets $9.31, BB folds

[Results: $13.00 pot ($0.58 rake)
Final Board: T A 6
BB mucked and lost (-$6 net)
Hero mucked T A and won $12.42 ($6.42 net)

Poker Stars, $1/$2 No Limit Hold'em Cash, 6 Players

BTN: $98.06 (49 bb)
SB: $101 (50.5 bb)
BB: $842.06 (421 bb)
Hero (UTG): $219.40 (109.7 bb)
MP: $206.42 (103.2 bb)
CO: $539.24 (269.6 bb)

Preflop: Hero is UTG with T A
Hero raises to $6, 4 folds, BB calls $4

Flop: ($13) 9 7 7 (2 players)
BB checks, Hero bets $6.21, BB folds

Results: $13 pot ($0.58 rake)
Final Board: 9 7 7
BB mucked and lost (-$6 net)
Hero mucked T A and won $12.42 ($6.42 net)

I don't like flatting open or 3bet with ATo but I like to open with it from anywhere.

Terp, please don't do it.