Would it make sense to encourage users
to answer questions in topics other
than their expertise?
I would argue that the system already does, if you are only willing to answer questions in your tight domain, the pool of questions available to you is a lot smaller than going wide.
I'm thinking about boosting reputation
The mechanics for this are way too complicated, and if you want to defend against gaming it would become more complicated still
badges for diversity.
There has always been the threat to implement the generalist badge, personally I think it would be a good idea to have both a silver and gold generalist badge. The tricky thing is figuring out who should get it.