[Phanx]

It would be possible, but a lot of work for no real benefit. Not only would it not save you, as a user, a large amount of time, but it would only be useful right after a major patch when lots of addons were updated at once, and many addons can break at once. The rest of the time, there's nothing happening to suddenly break your existing addons, and you're usually only updating one or two addons at a time.

Also, there's usually no need to do the "disable and reload" dance to figure out which addon is causing a problem; its name is right there in the error message that pops up on your screen.

If you don't see an error message, install BugSack. The default error display can't show errors that occur while you're logging in, and since that's when most post-patch errors occur, it's basically useless.

If you still don't see an error message, or the error message doesn't include an addon name (for example, it might be an error in Blizzard code, but it's caused by an addon), here's a simple procedure that will greatly reduce the amout of time it takes to check all your addons:

(1) Enable all addons whose names start with A-L, and dislable all addons whose names start with M-Z.
(2) If the problem does not occur, log out, disable addons A-L, and enable addons M-Z.
(3) Once you find the half of your addons containing the problem, disable half of those.
(4) Continue disabling half of the enabled addons at a time, switching halves as needed, until you narrow it down to one addon.

Even if you use 200 addons, this doesn't take very long because you're ruling out large numbers of addons at once.