I suspect that I can pull the wheel and change tubes about as quick as the "non-remove" method. However, the tube still has to be patched later. In my experience there have been several times when the cause of the puncture was not detected from the outside. Heck, I have had couple of times I missed it from both sides and had to patch the tube over again. I also line my valve stem with the logo on my tires to help locate the cause, but have still missed it.
And it isn't like I have not had a lot of practice.

I think trying to mount a really difficult mounting tire, would be awkward while wheel is still attached the bike.