There is a system for automatically setting the user agent in WebKit only for pages that need it. I would prefer using that rather than always changing the user agent.
Please complain to broken websites, they should not be doing user agent sniffing.
Note that upstream WebKit is also gradually removing things from the user agent to let less info about the user be traced.
Also, if it's only "theoretically", well... most websites already identify us as Apple Safari (the user agent is very close to that, on purpose) and I don't think we could make it much better than that. There are actual problems that prevent websites from working, in most cases.