I do this, using an up-to-date chromium browser proxied through Tor for regular browsing. I do this instead of the regular Tor browser on the theory that there's less potential for 0-day exploits.
Of course, this does compromise anonymity a bit in some respects, since there are probably few people who run chromium on Tor and because it's not as resistant to fingerprinting as the regular Tor browser. That's acceptable to me, as I only use that browser on Tor, and use another browser for things that could potentially leak my real identity.
It also opens you to many subtle mis-configuration bugs that would result in your anonymity being removed completely. Are you sure you're tunneling DNS over Tor? IPv6? Are you sure that Chromium isn't phoning home with your real IP?
Tor Browser (despite its many faults) has lots of patches that are applied in order to stop these sorts of leaks. If it takes the people who develop Tor to continually patch Firefox in order to make it actually anonymous, I would argue you have a worse chance of making it work properly.
> Are you sure that Chromium isn't phoning home with your real IP?
Especially given that Chromium does make startup queries to Google-owned servers. (Not sure about runtime.) Probably for perfectly reasonable usability and/or security reasons.
But I agree that Chromium manually proxied through Tor probably looks vastly superior to TBB when you do a benefit analysis. :)
Edit: added smiley to make what I'm saying slightly more obvious.
Of course, this does compromise anonymity a bit in some respects, since there are probably few people who run chromium on Tor and because it's not as resistant to fingerprinting as the regular Tor browser. That's acceptable to me, as I only use that browser on Tor, and use another browser for things that could potentially leak my real identity.