Your Proposed Solution
"Too many possible answers" is not equivalent to "too many answer posts are possible". Whether it's multiple individuals each giving a separate answer in their response, or one individual giving a complete response that contains multiple answers, does not matter. The "... or good answers would be too long for this format" part that you discounted is equally important, as well.
Limiting the response count does not affect this, it is only marginally related; just because the question itself has too many answers doesn't mean it must necessarily have too many responses, it just means that a complete response is potentially long and difficult to write. Your proposal is not really a direct solution to the stated problem you are intending to solve.
Additionally, if a question had many mediocre answers, and you arrived a little later and posted a complete, killer answer, the fact that your answer would not be displayed would be a loss. Your proposal creates an opportunity for damage but does not have a possibility for a helpful impact.
In any case, as it stands, SO limits the number of posts displayed on each page. Additionally, you can already choose to sort by top voted. This essentially gives the same effect as what you are proposing, except it allows users to view other pages and also gives the option to view newest posts first. The "page 2" button is equivalent to your "show more" button. It is a superset of your proposed change.
Also, if an answer is accepted, it is displayed at the top.
Your stated root problem is extraneous noise due to poor answers. I personally don't see this and I think it would help if you included a few good examples of where you see this.
For the most part, over time, vote counts on answers will naturally sort them by quality (roughly). I believe you are forgetting that most people have the ability to read through the answers until they find an appropriate one -- when they do, if they upvote it, it will move the answer up in the ranks.
The real best solution is for you to continue making good use of the voting system. If you see a good answer, upvote it. If you see an incorrect answer, leave a comment on it and possibly downvote it. If you see an answer that breaks the site rules, flag it. Consider it part of your responsibility to vote and comment on existing answers in order to improve the overall quality of information for the community as a whole by helping to move "noise" further into the background. If you use the tools that already exist, then it benefits everybody.