Just plain glue and clamps provides plenty of strength. Adding an internal profile to create a glue joint doesn't really add much surface area. It may, OTOH create weak edges.
As an example, I've made raised panels, using plywood for the "field", and wood edging, wide enough to use shaper profiles. This provides for a "no movement" issue for a raised panel, and long grain instead of end grain on the ends of the panel. Never had a problem with the edge. Likewise, made doors possibly like you're doing, with plywood and a wide wood edge, that carried the whole cup mortise, and then some. It was also for a wide detail on the face.
I hear the descriptions that some on forums describe on their extensive machining of some glue joint, biscuit, or pocket screw mounting for FF's to carcasses. If the back of the FF and the leading edge of the carcass are flat, glue and clamps works well. BTW, most all my cabinets are frameless, unless a FF is called for to match existing work, or needed for a design detail.