I've heard of guys sparging and lautering for over 3 hours using a traditional mash tun. With BIAB, I pull up the bag, let it drain for about 5 mins, press the crap out of it on a grill for about 5 minutes and all this while my burner is going full tilt to get me to boiling. So, based on what I've heard (never used a mash tun myself) I think can be a huge time saver, especially with grains that are prone to getting a mash stuck.
Ok so I can understand that misconception (that same technique is what scared me from AG in the beginning). Using batch sparge techniique I routinely bang out 2 10G batches in about 5-6 hours.
I would venture to say the vast majority of folks batch sparge (I could be wrong).
After mashing, open your ball valve all the way and let wort drain off.
Batch sparge Add in water, not to exceed 168F, to make up your preboil volume (if you get 5 gallons wort and your preboil is 13g, you add 8 gallons to the tun). Stir the grains for 1 minute and let it sit for 2 minutes. Open ball valve up full throttle and drain into Boil kettle.
My batch sparge takes 3-5 minutes.
I know the way you are talking about as traditional. Many folks may do that, but I think that is more old school. Batch sparging is quick, gets you high efficiencies (76-78% is my usual).
As for stuck sparges,... not in a blichmann tun as far as my experience goes. I have done a lot of wheat and rye brews this year (I only do 10g batches). No stuck sparges to date.
The only major savings in BIAB IMO is the cost of a mash tun. For that reason though, I think that is why it is so clutch to getting extract brewers into the AG game. The low equipment cost makes it accessible.
The tough part comes when you try to up your grain bill. Imagine a BIAB with an IPA grain bill for a 10G batch. Get the pulley system out to lift that bad boy up!