Hmmm, well TREZOR requires a web plugin. So if nobody installs plugins then we have a problem :) But regardless, actually like I said, you don't need a plugin. Browsers do it all already. With the <keygen> tag they even create a private key and upload the public part to be signed for you, it's seamless for the user. I wanted to give you a link to a demo site, but I can't find it anymore :(
So there's not even a need for people to upgrade anything! It's all there, already, for everyone.
If you were to make some upgrades, then you'd want to focus on key management, which indeed is something the Bitcoin world is trying hard to solve. But that's a small subcomponent. Making a modified version of Chrome or Firefox that can take their key from a BIP32 hierarchy or 12-words scheme is certainly possible, but then you could still reuse all the rest of it.
Something I'd really like to see is TREZOR supporting a simple request/response protocol that a server can trigger, via the USB plugin, that would allow a server to display some arbitrary text and get a confirmation. Slush and I talked about it before. There are a LOT of places that don't care about Bitcoin but do need some kind of safe second factor auth where users know what they are confirming (e.g. at Google!). If TREZOR could be used for these things too, that'd increase demand and help push down prices for Bitcoin users.