From my experience, uninstalling Flash will let you see _less_ missing plugin icon than having Flash installed with Click-To-Play enabled. This is because once Flash is uninstalled, the browser will simply report to the website that the user do not having Flash and allow the website to fallback to no-Flash mode accordingly.
One biggest problem of having Flash and using Firefox was Vimeo videos because Firefox weren't able to play H.264 on its own, and Vimeo do not provide WebM. This is where it used to be the problem. However, fortunately recent Firefox versions now included OpenH264 codec and could play Vimeo videos without any problems.
Nowadays there are only handful of sites I need to keep Chromium installed, but the number is rapidly decreasing. With YouTube switching to HTML5 by default, I'd recommend anyone to try uninstalling Flash and rely on Chrome/Chromium when Flash is needed. You won't really miss much.