Where do you think Gavin's salary comes from?
There is a strong business case, he's coming up with a decent solution for it, and because his paycheck comes from the foundation rather than a specific company he can come up with a solution that can be used by everyone in the community and doesn't privilege any particular player. (except certificate authorities, initially, but the payment protocol is pluggable and more decentralized PKI systems can be easily added later as they are developed)
The payment protocol is a pet project of Gavin, that will be useful just like everything he makes, but has not much to do with the core of Bitcoin that should rather be hardened and standardized as it was originally postulated to be the purpose of the foundation, that pays his salary
There's plenty of very intelligent people working on understanding and improving Bitcoin's core technologies and resistance to attack. What we're lacking most is people doing the ugly and boring work, and the payment protocol definitely fits that description. Heck for me personally even testing and auditing, at least for cool stuff like security and consensus threatening bugs, is way more interesting than the payment protocol.
Anyway, Bitcoin is brand new computer science and cryptography and you really don't want a single person being "assigned" to hardening it and refining the design of it. No one person is smart enough or has the breadth of experience to do that, but from the sounds of it the Foundation doesn't have the money to hire the teams of researchers that you'd really need. So they're doing a good job focusing their efforts on what they can do, and letting the community handle the rest.
Gavin works on whatever he likes, just like all other core devs in my observation.
I believe that the criticality of payment protocol is way below of other issues and if it was business critical there would be funds for it other than the foundation's.