BIAB CAN contain a sparge step, those saying it can't are just been purists who believe that it's only BIAB if you don't sparge... Personally, I see shooting yourself in the foot re efficiency just to be a purist as silly. There are plenty of guides to BIAB that include a sparge step. BIAB just means brew in a bag, and that's exactly what you are doing even if you sparge. There are quite a few variations of BIAB.
For every definition on the internet saying that BIAB is ONLY full volume mashing, there is at least one other saying that you can add a sparge step etc and it's still BIAB.
Apologies I feel you may have taken a bit of an offence there.
It wasn't meant as a purist comment, I typically interpret it that way because BIAB was designed for a single vessel system which involved a full mash system of course you can add in any extra stage you want. Nobody is saying you can't sparge, just typically you do not with its original concept which was a single step process in a single vessel. Adding a sprage by seperatly heating is fine but it typically would require a second vessel to heat in.. not a problem either way. I wouldn't get too hung up on it you could add 50 steps if you want to.
I used to sparge and I now for this I don't it isn't about being sensitive about being purist tradition it is about being a simpler process and consistent.