I agree. The middle ground is better than writing no tests.

I do think it's more than a few minutes though. The problem is when you do a big rewrite you've now sometimes got a lot of failing tests. Do you go back and delete these tests and write new ones? Or refactor the test code? It's just a big distraction because sometimes you're "holding the program" in your head, as PG would say, and to worry about tests might cause you to lose your focus on the more important code.