You're 100% correct that the other answer-based websites and apps have little to no incentive to do a good job on writing solid answers to people's questions. This seems like the perfect way to use Steem. I spend little to no time on sites like Quora, Sli.do, and Yahoo Answers, but I may be inclined to use this app.
As an afterthought, you definitely will have trolls that try to come up with the funniest replies, but that might be part of the fun in the end!
Great idea! Hope it turns out.