so many good and updated answers are somehow pushed to the bottom by these verbose answers.
No, those answers are 'pushed to the bottom' because they have less votes than the verbose answer, not because the verbose answer is longer. In theory, this should mean those answers, when posted at approximately the same time as the verbose answer, aren't as good as the verbose answer, or they would've gotten more votes and floated to the top instead.
I realize this isn't always true for old questions and/or outdated answers, but there's a whole project focusing on those already, and I don't think showing only bits of existing answers is going to help in determining whether something is outdated or not. Especially not as long as users include updates at the bottom of their answers, which I personally see happen way more often than updates added at the top. In cases of updates like that, an answer becomes longer the more it is updated, but the most relevant information would be hidden by a 'read more' button.
Also, on more subjective sites one rule of a 'good subjective question' is that "Great subjective questions tend to have long, not short, answers.". Limiting the size of the answer shown on such sites, and hiding parts of them behind a 'read more' button, goes against the spirit of that rule: Why encourage writing longer answers with sufficient back up and sharing of experiences, if all that's going to be shown is a first few lines? Answers should be evaluated in their entirety, and not just on the click-baityness of their first few sentences.
One more argument, related to the one above about the click-baityness of the first few sentences: As a moderator, I regularly see votes reversed because they are cases of robo-voting to earn badges, votes for a specific user, or sockpuppet voting. The reason all of these forms of voting are 'offenses' that will get you at the very least just a message and vote reversal, but also likely a suspension, is that these votes weren't made for the content of a post. If parts of answers are hidden behind a 'read more' button, clicking that button becomes an 'impediment' to fully evaluating the content of a post before voting.
I was wondering if introducing a read more button for long answers could improve the discoverability of new answers and improving the overall reading experience.
Given the arguments outlined above, I don't think a 'read more' button should become some sort of default situation. Newer answers aren't by definition 'better', and new answers can already be easily discovered by sorting, like Shadow's answer outlines.
It also wouldn't improve reading experience, at least for me having to press a 'read more' button interrupts my reading. Together with the potential downsides described above, I don't think a 'read more' button and the one or two scrolls it might save will be beneficial.
Finally, a read less button at the bottom of the answer could also solve Move the vote button feature request, allowing you to get straight to the top of the answer where the vote button is.
In that case though, instead of having people first click 'read more', and then 'read less' again, just following the original feature request, or perhaps just having the vote buttons visible all the time (make them scroll down when you scroll through a longer answer?) are probably still better options than first having to introduce a 'read more' function just so there can also be a 'read less' one.