This is a great idea, but one that is probably going to be extremely hard to implement properly on Wikipedia.
Unlike traditional texts and even many online texts, Wikipedia content changes often and sometimes drastically. Sometimes the underlying text you have highlighted may have disappeared completely, sometimes a few minor changes will make it very difficult to map you old highlight on the new text.
I think it would be best to copy any highlighted text into you bookmark list (Bookmarks/read later) and then make a best-effort attempt to map that copy back onto the current version of the text. If this attempt fails, then you will at least still have your copy.
Having more accurate information available on how text changes from revision to revision (more accurate than a line-based diff), may also be helpful for that purpose.
Public highlighting may have privacy implications (some people may not want to use this tool if their highlight may become public, the minimum number of highlight needs to be quite high to guarantee anonymity, ...), moderation/biographies of living people/neutral point of view/undue weight issues (e.g. a coordinated external campaign to have multiple people highlight some controversial parts of a politician's life on their biography?) and general lack of quality or relevance (e.g. my Kindle does exactly what this feature is describing: if a sufficient number of people highlight the same sentence in a book it will show up for everyone. Typically this is one sentence on the first page and sometimes a random sentence in the book. Maybe it will work better for non-fiction, than fiction, though?) Showing public highlight for text that is no longer in the current version of the article would be a very bad idea.