I agree with everything you said except one bit.

> In my experience, someone who refuses or takes offense at a well-framed coding exercise is probably not going to be someone you want on your team.

In my experience those who refuse are the top of the top. We adapted our interview and intake process to accommodate these people (usually with a more stringent and goal oriented probation period), and it was the best thing we did in terms of resourcing. The people we took on through this stream ended up being by far the best performing bang for buck employees. They are opinionated and snobby, but that's a good thing, because they actually care about their respective fields enough to have strong opinions. They don't waste time with tests and coding challenges.