I think it's going to be a lot of hassle and even if it's implemented, people will still need to make edits in their posts even after using the "quote single" button as you suggested. Let me explain why.
I know this can make quoting a bit easier for those who are willing to quote only the last text done by the user they are quoting, but only if the last reply only has one text with no extra elements or multiple quotes. For example:
If you are quoting me but my post has multiple quotes each placed one after the other in this order:
First paragraph of your post
My response
Second paragraph of your post
My response
etc.
In such a case, the user will still have to do a lot of editing to remove the portions of the post he isn't willing to respond to, just like how a person would do with unnecessary quotes.
Another issue is about other added elements in the last post you are quoting. What if I'm quoting you as your post is the last response but your response contains quotes that are added by yourself maybe to add some other information or a reference or anything in general? For example:
your post - What would ChatGPT's response be if you ask it about Bitcoin's price in 2025?
My response - I have tried that and below is the result:
ChatGPT's response
Now, if I use the "quote single" button, it might remove the extra quote tags along with its content as well but it isn't supposed to do that because it's a part of the response and isn't a quote from another user that I might not need.