Test plans never account for everything, at least in my experience, especially edge cases. And it's rare that I've seen any QA team do a full regression test of the entire site. There's only been a few times where I've seen it authorized, and that's usually after a major refactoring or rewrite.

I'm not in QA, I write code, so I defer to whatever they decide for these things usually, these are just observations from what I've seen.

I just try to make sure I test my code enough that there isn't anything terribly broken when I check it in and fixes I need to make tend to be relatively minor (with a few exceptions in my past).

Also I'm not necessarily talking basic functionality here. I'm currently working for a client that's very picky about the look and feel, so if a few pixels in padding get adjusted where it's noticeable, or a font color or size gets adjusted a bit, in one place and it affects something else, there could be complaints. And a test plan is not likely to catch that, at least not any on any projects I've worked on.