"... so the fact alone that you're unique might potentially not matter if you're _differently_ unique every time you visit the site. Is there a flaw in this line of thinking?"

No, you're thinking correctly and the odd discourse that you (and I) see is based on two implicit assumptions:

1) Your threat model is a global observer that notices - and tracks and exploits - your supposed perfect per-request uniqueness.

2) Our browsers do not give us fine grained control over every observable value so if only one variable is randomized per request, that can be discarded and you are still identifiable by (insert collection of resolution and fan speed or mouse jiggle or whatever).

Item (1) I don't care about. I'd prefer per-hit uniqueness to what I have now.

Item (2) is a valid concern and speaks to the blunt and user-hostile tools available to us (browsers, that is) which barely rise to the level of any definition of "user agent" we might imagine.

I repeat: I would much prefer fully randomized per-request variables and I don't care how unique they are relative to other traffic. I care about how unique they are relative to my other requests. Unfortunately, I am wary of browser plug-ins and have no good way to build a trust model with the 12 different plug-ins this behavior would require. This is the fault of firefox and the bad decisions they continue to make.