Even on a frame, quilts don't have to be "quilted to death". You can do minimalist quilting FMQ or on a frame (I do). There's no reason you can't satin stitch the applique on the quilt you are looking at - do what you like! I don't like raggy edges either. You can also turn almost any applique into a needle turn or something else without the raggy edges - but satin stitch would take care of that nicely too.
SITD is always an option, or echo quilting just inside or outside the design.
My "go to" options are: large meander (for wide open backgroud spaces, or an all-over design); SITD; cross hatching (about 2" apart is my preference). I'm branching into more 'custom' designs, following the block pattern, but I still like a lightly quilted look, so I stick with something that is 1-2 passes over any piece in the quilt.