The ‘problem users’ that I’ve had to deal with in my time were problems because they want either rep (/more upvotes) or power - mostly the former (albeit possibly as a way to get the latter). Getting rid of rep and introducing a better voting system should get rid of most of this.
Ultra high-rep users have a tendency to be very quick to answer questions (because answering first gives you the rep first and prevents others from answering) - there’s nothing inherently ‘wrong’ with this but it does lead to fundamental issues on the thinking of how the site works - my best answers have been the ones where I’ve had to do the learning in order to teach, so I get as much use out of the question as the questionner got out of my answer. If there’s already an answer by a high-rep user, I’m much more disinclined to answer and so, learn less, defeating the point of a community for learning.
In addition, the above leads to extra competition, which tends to lead to ‘putting people down’ and ‘beating the other person’ instead of ‘lifting people up’ and ‘encouraging the other person’.
It makes the other important stuff less noticeable (e.g. editing, flagging, reviewing, cultivating the site, using comments to clarify and improve questions etc.)
A number by itself doesn’t say whether someone got that number by answering lots of easy questions (i.e. is quick at answering questions) or by answering lots of harder questions (i.e. is an expert, at least in some sense). It also doesn’t say what they’re good at. In addition, there are some amazingly wonderful people who don’t have the same rep, yet can be just as knowledgeable and good at answering questions as someone with loads of rep, perhaps because they answer stuff on an obscure tag.
If you can loose rep for being wrong, why risk being wrong? Yet being wrong is a part of life, something everyone needs to learn to deal with and an essential part of the learning process. Being wrong is bad for getting the right answer. Being wrong is good for learning.
The ‘HNQ effect’ where people would write controversial things and clickbait for the sole purpose of getting upvotes and rep. I like neither of these.
the “Someone downvoted me, so I lost reputation, so they’re unwelcoming!” misconception. (Perhaps conflating votes with rep a bit here, but votes and rep are explicitly tied, so they’re hard to separate) Whoever had the idea of a system called ‘reputation’ and a way to loose reputation may not have thought about the consequences that ‘loosing reputation’ in real life is a very bad thing, so people are naturally going to consider this a bad thing online as well. Perhaps even the choice of word used matters?
The above may lead to fewer people using downvotes as much as they should.
It places the emphasis on something other than what we want the emphasis to be on and heavily related to this, it provides an extrinsic motivation. I’d like a psychologist to confirm this but I’m led to believe that if anything, extrinsic motivation doesn’t generally last long and often decreases intrinsic motivation.