These interviews do filter out any engineers that can't solve these algorithm problems on a whiteboard, but they don't necessarily filter out people who have a proven business track record and can get projects done on time and under budget.

I think the phrase "jack of all trades, master of none" is overused and doesn't hold a lot of truth. It's very possible to have a lot of experience and skill in many different areas. Maybe there's even a positive correlation between being a very good programmer that can pass whiteboard interviews, and being a pragmatic, get-it-done type of engineer.