A LAV without a turret would be smaller and lighter than one with, which would make the LAV somewhat more mobile both tactically and strategically. How much of an advantage this would be overall is a matter for debate.
I am starting to wonder if we are getting overly wrapped around the axle over the entire vehicle thing; being tied to the roads is NOT a good thing in counter insurgency or conventional war. The destruction of GM-100 in French Indochina is a salutary example of what can go wrong, and the American experience in Mogadishu extracting TF Ranger from the snatch operation with a road bound convoy shows that although armour protection would be a plus, command and control issues are probably even more important (the convoy was under observation by a PC-3 Orion throughout the mission, but the convoluted communication chain meant that directions from the Orion were relayed to the convoy too late). An armoured vehicle disabled in the road would have stopped TF Ranger in the way disabled HMMVW's did not (they were pushed out of the way or down the road by following vehicles), but that falls into the realm of "what if".
We need to reduce the "footprint", and use our armoured vehicles more like a "cavalry" force or QRF. Our forces might take a page from Robert Kaplan who writes of American forces moving around Afghanistan in Toyota pick-up trucks.
Some thoughts