I mash 3-gallon BIAB batches in a 5-gallon beverage cooler, and boil in my 5-gallon kettle. Fermcap is required to prevent boilovers, but otherwise it is quite manageable.
I can actually do that (I have a 5-gallon cooler I stopped using when I got a 9-gallon Coleman Xtreme) but I'm curious what I'm getting from this procedure that I don't get from my setup and process, aside from upper-arm exercise. I went no-sparge a few batches back and haven't looked back. So BIAB would be the difference between lifting a bag out of a cooler and transferring the cooler's contents into a kettle, versus opening a ball valve and draining into a kettle (I often do push the boundaries and boil 4 gallons in a 5-gal kettle using Fermcap). The bag won't magically transport its contents to the compost bin, so it needs to go somewhere, and that somewhere will need cleaning as well.
I went the separate cooler mash tun route because I'm lazy and didn't want to deal with monitoring mash temps if I left everything in the kettle. Otherwise, the main advantage of BIAB is that it's a 1-vessel system, so there's no additional equipment beyond the bag.
For me, what I like about the bag vs a manifold/false bottom/bazooka screen is that there's no dead space and less grain absorption. Since I'm only mashing in a 5-gallon cooler, that added efficiency boost lets me brew some bigger beers using my normal setup without having to take extra steps (like adding DME). But frankly, why I really like my system is because I worked it out myself, and because it works well for my purposes (i.e., brewing 3-gallon batches indoors).
Also, if you did want to batch sparge, you could certainly use a bag the same way you'd use a false bottom or screen.
In general, BIAB isn't necessarily a solution to improve all-grain brewing for someone who already has a setup that works for them. But it is an easy way to step up from extract brewing without having to buy a lot of new equipment. It is also quite well suited for brewing smaller batches. If a brewer typically brews 10-15 gallon batches, but wants to brew a 2-gallon pilot batch, then BIAB is a simple option.