Actually there is a major class of problems people have where they are so stuck that they don't even know what question to ask on Stack Overflow. Being able to ask a question live, and get immediate feedback, and have a quick conversation with someone more knowledgeable than yourself, before (or instead of) asking a question on Stack Overflow, will allow programmers to get help with a whole new class of problems.
And of course, that's in addition to the "social hang out" feature that chat provides to the Stack Overflow community.
One of the big things StackOverflow has going for it is permanence. Someone asks a question, gets an answer and then google indexes it for the next person who has the same problem.
With the chat it will fix the problem for 1 person but the scalability of investing your time into an answer that could potentially help a lot of people over time is lost. Even if google indexes all of the chat conversations reading through a chat transcript looking for the answer is tedious.
There's no way to expect that the SEO for chat archives could possible provide this.
Is this a good thing? Personally, I don't know, nor would I care, how to implement a reputation system in chat. But I would hope that the answers in chat would be of the same caliber as the static questions.
Yes, there is. In fact, it's the same basic incentive that people have to answer questions on StackOverflow: to help people. The reputation system is a nice plus, but I'd hardly call it a deal breaker for it to be missing.
In order to accept your premise, you would have to agree that there is a certain class of answerer who, when presented with a question in chat, would think to themselves "gee, I think I know how to help this guy, but I'd really rather not help him since I'm not getting quasi-meaningless points on a website".
You've always said that the primary audience for StackOverflow is Google. The premise being that the site will accumulate a collection of good answers to common (and some uncommon) questions, so that the second person to ask that question won't have to. The impermanence of the chat system defeats this premise utterly.
It's also odd to see you responding negatively to a comment (i.e. negatively towards questions in chat, not the commenter) when that comment was in response to Joel himself saying chat is the best medium to ask certain classes of problems.