Okay so bear with me, and please feel free to ask questions or clarification.
The difference due to grain absorption rate is not really due to conversion differences, but lauter efficiency (in braukaiser terms, or in BF terms the lauter efficiency can be thought of as mash/kettle efficiency divided by conversion efficiency).
What you may not be taking into account is that when comparing two equipment and process types, you don't get "extra" volume, but rather you start with less water. Since you're starting with less water, you're result will be a higher SG in the mash. The net conversion efficiency will be around the same (assuming you don't run into issues with mash thickness or mash pH in the mashtun).
It's easier to compare side by side in my biab calculator IMO, but Doug293cz on HBT would also be a great resource for this. He helped me a ton when I was starting to integrate braukaisers efficiency formulas and mash models. I've since re-derived from first principles using a SG model instead of converting back and forth from sugar weight to brix/plato to wort weight etc etc but that could be a 10 page dissertation so I'll leave that alone for here...
In general BIABers get an average of 0.08 gal/lb absorption rate, vs an average of 0.125 gal/lb for mashtuns or process where you don't press/squeeze/suspend the grains and just let it drain without lifting.
Scenario: 1.065 OG, 5.5 gallon batch. 1 gal boil off. ~95% conversion efficiency. no mashtun losses or kettle losses. The only difference will be the expected grain absoprtion rate (and therefore the total volume of water needed).
A: Mashtun, equal runnings between mash runoff and sparge runoff volumes (this is ideal peak efficiency for a batch sparge).
12 lbs of grain, 1.55 qt/lb mash thickness.
Expected efficiencies and gravities:
Same recipe with BIAB, changing the absorption to 0.08 in my web app, with no other change.
So for this particular scenario, we can expect roughly a 4% loss in brewhouse efficiency, largely due to the lack of a sparge.
Now if we do BIAB, with a squeeze for lower absorption, but ALSO a sparge,
Here we get an even higher efficiency than the mashtun with sparge, since there is less water used in total.