(I'll note that I have no problem pairing in real-world work scenarios! I love discussing problems with my team. It's the artificial pressure injected by the interview process that really gets to me)
I don't have issues with whiteboarding and pair programming with my current teammates. I can speak up and have enough confident to do. But its not the same in an interview situation. I prefer take-home as well.
I still struggle with the "observer effect" during live extension exercises, but it's less pronounced than when starting with a problem from scratch. If I prepare a high quality solution in advance and do well in technical discussions, that's usually enough to offset any fumbling around during the live programming session due to interview jitters.
If you have an unlimited engineering budget or a big, attractive name then by all means, force candidates to jump through as many hoops as you'd like, you'll still be able to fill open reqs. But the majority of companies are not in that position and in fact struggle to attract and retain technical talent.
+1 Vote