Acoustic Panel Room Treatments : Built-in vs surface mount question

If one were remodeling a living room or other multi-purpose room where, upon completion, a 2-channel system was going to be, holding aside local building/fire safety code issues, are there acoustic reasons not to install sound absorption panels, like 4” Owens Corning 703 fiberglass insulation or whatever products a place like GIK sells, as inserts into cut-outs to the walls and ceiling (5/8th” dry wall) so that the net result is sound absorption that is flush with the walls/ceilings (and ideally could be skim coated and painted so as to make the whole surface look seamless) as opposed to surface mounting the absorption panels?  Does the raised and lowered profile of a wall or ceiling with surface mounted panels do something beneficial acoustically that a flush surface with embedded panels would not?

Thanks!