I would find some kind of ignore/mark user functionality incredibly helpful primarily to make enforcing my personal do-not-answer-to-this-one (to use the the nice name @CarLaTeX invented) list easier, which is important because this is the only real lever(*) I have for users who (in my personal opinion) do something wrong.
(*comments and downvotes don't really have any effect, they are often just ignored)
Why an ignore/mark functionality cannot be replaced by moderator actions or bans?
There are three kinds of users who end up on my do-not-answer-to-this-one list
users who ask question after question without upvoting or accepting the nice answers they got to their previous questions. I usually leave a comment below their previous questions explaining how and why to accept an answer and if I encounter this user again and no answers have been accepted (or some other reaction, like the answer does not solve the problem because xyz) I add these users to my list because this shows that these users don't appreciate the time and effort we put into answering their question
users who continue to post questions without MWE even after having been asked to do so multiple times
some other triggers, which can be summarised as "users who don't appreciate that others sacrifice their spare time to help them for free" (this is a bit vague, but various strange things happened which don't fit into a narrow category)
This clearly shows that not all behaviour that (in my personal opinion) is incorrect behaviour of users is something that mods can help. Not accepting answers, ignoring comments etc. is all perfectly in agreement with the rules of this site, it is just something I personally don't like and I think the other options provided by the site (commenting and voting) are not as strong as not answering questions of this special kinds of users.
Luckily this only affects a tiny fraction of the users. From the 145 000 users of tex.se I have 22 on do-not-answer-to-this-one list
Experience with ignore/mark user functionality
22 names sounds not so much, but with cryptic user names like user123456789 (dummy example) they are nevertheless hard to remember. Therefore I used a browser addon in the past, which would mark posts from users on my list with a red rule so I can easily notice.
(The addon I previously used was https://bures.io/products/favorite-users/stack-exchange/, unfortunately the new "responsive" site design broke it and it no longer works for questions and causes various formatting issues)
The main effect was that I was much more relaxed. My default assumption was that every user was well behaved unless the post had a red rule besides it and if the question itself was reasonable posted it should have an answer. This made spending time on tex.se much more enjoyable.
Now in the post
apocalyptic new design world, there is this constant subconscious fear that I might be giving answers to users from my do-not-answer-to-this-one list (which is probably my own fault because I'm often too lazy to check each and every user name if it is on my list).
Reasons against an ignore/mark user functionality
I see two main reasons why this is a bad idea
the philosophy of stackexchange always was that all actions (voting, answering etc.) should be based on the post itself and not the user, that all users should be treated equally. IMHO The Powers That Be broke this rule themselves by these "new user" warnings signs in triple occurrence, so I don't consider this a valid reason anymore
the mission is larger than answering the question of a given user -- the aim is to also build a database of knowledge for future users. I think this is a valid concern. Personally I would therefore prefer a way to mark users instead of completely hiding the questions, then one could make exceptions if a question sounds useful enough for future users.