Why is "Whataboutism" often criticized?
"Whataboutism" is criticized because this is a way to escape an issue rather than to discuss an issue, and that's why that most of conversations start at a point but they would never end where they've been started, when someone uses this technique it means they have no justification for their acts or false claims and by bringing up a weakness or controversial issue mostly pertaining the second party of the discussion they try to hide their own weekness at responding. (Please note that I'm talking about general situations not particularly Russia and America or the war in Ukraine)
This would be a successful attempt to escape if you know what to bring up, if you can bring up a very sensitive issue that the second party can't leave alone you have changed the course of discussion but it necessarily doesn't mean that you have won the discussion, when you bring up something sensitive about the one who is criticizing you, you can actually make the conversation to backfire cause the second party would try to acquit themselves from the alleged charges so your wrongdoing is forgotten.
This is criticized cause it never answers the question in the minds of the audiences, like your example, the US says "Your crimes in Ukraine" and Russia says "what about your crimes in Iraq, Vietnam and....", Russia is actually pointing out an important issue because horrific things happened in Iraq, Vietnam and other places, but the question is not answered and the issue is just screwed.
So if Russia is really doing those alleged crimes, the point that the US has attacked many countries itself and killed many people doesn't justify the crimes of Russia and if Russia isn't really doing those crimes so why don't they bring up an evidence and prove the falsehood of the words of the US? The fact that the US attacked Iraq for the phony pretext of WMDs doesn't give any permission to Russia to do the same.
But there's still a point that should not be overlooked and that is can a criminal be a witness? If a drug dealer that is arrested can't be a witness for the crimes of his gang so who can be? (Again i'm saying that I'm discussing in general not specifically about Russia and the US), the fact that the guy himself was a drugdealer doesn't make his words about his gang useless that if it did, why the detectives interrogate the person to make him rat on his gang?
So we can't really say that if the person X is a criminal, that person can't accuse the person Y of a crime. But still this is the pot calls the kettle black. If the US killed people in Iraq it doesn't mean that they can't condemn Russia for killing people in Ukraine. (this is just an example, I don't claim Russia is really killing or not), but of course if you think someone is doing a wrong thing, you shouldn't do it yourself, that if you do, then you're a hypocritical guy.
This is actually true about both parts, if Russia condemns the US so why itself attacked Ukraine? And if the US condemns Russia why itself has attacked many countries? And that's why the pot calls the kettle black, but again it doesn't mean that the pot or kettle aren't black!
As user366312 says, "A criminal can be a witness, but a criminal can't be a judge." the fact that the US can criticize Russia doesn't mean that the US has any right to punish Russia too, as I mentioned in the comments, you can't wipe off a dirty window with a dirty cloth, if we want to punish, we have to have an impartial third party that punishes both sides cause both of the drugdealer and his accomplice have committed crime.
Those who criticize whataboutism, What better type of reply do they suggest?
As I mentioned above, the best answer on behalf of the party which is being accused is to bring up evidence to prove the falsehood of the charges, or else by screwing the word they only leave an unanswered question in the minds of the audiences which would cause distrust.
This is like whe Russia says I have attacked Ukraine cause they were neo-Nazi, I( supposedly) come up and say, so what about the crimes of the Soviet Union? This is pretty absurd, the right thing is to ask Russia if you claim that they are Nazis, can you bring an evidence to support that?