Upvotes are an indicator of quality, not a guarantee
I'm working from the assumption that typical WB users don't have a ton of time to spend here (but the following holds for heavy users in a slightly different way). A user wants to read good questions and good answers. If upvotes were removed from the entire site UI, then a very handy indicator of question and answer quality would vanish.
Most questions are not very good, as is true with most things. The average answer has just under 8 upvotes. The average question has only 5 upvotes. If I have to choose between two questions of equal age where one has 10 upvotes and the other has 2 upvotes, I'm more likely to chose the 10 upvotes. I know that 10 other people somewhere thought that the question was good enough to confer a little love. I may come back to the 2 upvotes question.
Said another way, upvotes are a proxy for quality/popularity. Without upvotes, individual users must hunt through thousands of questions to find a few that interest them. They must read through each question and answer. Ain't no one got time for that. Certainly, relying on upvotes alone doesn't work so well; no kidding, you've discarded a great deal of valuable information to get down to that single number.
Sure, there's some "well everyone else upvoted, so it must be good" that happens. I'm sure I've done it as well as everyone else on Meta. I choose to believe that the influence of this is pretty small. If a question is legitimately good, I'll upvote it. If it's truly awful, I'll down vote it. In the middle? Meh. I'll leave it alone.
I don't think there's anything to worry about with visible upvotes. Not having visible updates introduces a ton more problems.