"I personally find recording while wearing headphones to be very unnatural."

Fair enough. I agree - I have horrendous problems playing with cans on, especially on cello. Apart from the fact that it just feels weird and they physically get in the way (the latter is less of a problem with other instruments), it's well documented that our hearing of pitch is bent by varying sound levels, and inexperienced players don't know to be fussy about sound levels in headphones - time getting that right is well spent.

Playing to a click track is another nightmare, one that I've got slightly more used to but it's still an unpleasant experience.

The advantage of recording that way is that repairs can be done afterwards, but it takes a lot of time.