When I went from AG to extract I considered BIAB but my stove can't handle full boils with my Blichmann 10G pot so I first had moved my brewing outside and onto a propane burner.
I went with the traditional route for a number of reasons, and I don't really use an HLT but rather a second pot for heating of sparge water. I do all my mashing indoors and it's fine with my cooler as it traps in any odors - the mother-in-law always complains incessantly about any stove top grain cooking smell. Anyhow, onto the reasoning:
1. I didn't want to have to lift out a heavy bag of grains and suspend it while it drains
2. I HATE cleaning out grain bags, especially bigger ones!! It's a pure PITA in my opinion
3. I worried, and I still think rightfully so, that the Blichmann burner would torch the bag unless I could find a way to suspend all that weight
4. I've read several BIAB brewers claim lower efficiency
5. If I used a pot for mashing indoors the smell would permeate more throughout the house and I'd have to hear the complaints. Doing it outside in my kettle I knew would be much harder to maintain mash temps in this weather, I would need to apply heat every now and then
6. The extra cost wasn't a matter for me at all and I personally find it more convenient in several ways
As for the stuck sparges and all that, I don't have any. I had a stuck sparge when I first went AG because I'd gotten a false bottom for my cooler. I had to basically move the grains over to a grain bag and it turned more into a BIAB. But, I found out right after the brew the false bottom was warped. I returned it for a refund and got a bazooka screen for $17 and it's been awesome with no stuck sparges since. I very rarely use rice hulls too, never do with my wheat beers, but I have used rice hulls on a few occasions to play it safe. I mill my own grain and I've been getting a consistent 79% efficiency since getting my own mill.
Do whatever makes you happiest, it's not really a matter of this vs. that in terms of what's better. It really all comes down to a "configuration" that works best for you. Some people do it on their stove top and BIAB is most convenient. Some do it for the cost savings. Others have reasons for using a more traditional setup - and trust me... most of us aren't doing it for "traditional" reasons. It just works best for me and the way I brew.
Rev.