I have done BIAB about 5 times and batch sparge about 15. One big benefit of no sparge BIAB is you only have to heat one pot of water. I heat 8 gallons of water to strike temp, add grains, stir, and then wait 1 hour before removing the bag.
With batch sparge I heat strike water, add grain, stir, wait one hour,then heat mash out water, stir, drain, then heat sparge water, stir and drain.
Heating three pots of water versus one is but annoying.
The total water volume is about the same either way so there is no difference is propane cost.
It's just a simplicity thing.
PS. I do both methods because I think both are pretty cool. I love the engineering part of brewing. I have done fly sparge a few times to.
Who said you had to use hot water to sparge with? I use cold water and not too much of it and the hot grains heat the water to improve the solubility of the sugar. I find it easier as I don't have to heat the water nor do I have to worry about splashing the hot water on myself. You should try it once and see how it affects your efficiency. I also don't do a mashout because as soon as the bag of grain is out of the pot the burner is on to heat to boil. That accomplishes the mashout. One pot, one bowl to set the grains in while they drain and I'm mashing.