There have been a few semis with rear control plates, but it's quite time consuming to make a control plate to fit an arched back (or front). So that would probably put the cost up more than people would pay. the Gibson Midtown is a 'semi' with a rear control plate, but it's got a flat back and is really a hollowed-out piece of mahogany with an arched top stuck on the front. Also the Gibson BB King Lucille model (as that has no F holes). And the ES-333 (Custom Shop only though there was an Epiphone Tom Delonge 333 model).
It's going to affect the sound a bit, the back won't vibrate in quite the same way. You'd need to either use very thick ply so you could rout a lip into it for the plate to sit on and still have enough depth of wood for a screw to grip (very unlikely it would be done that way), or you've got to cut a hole in the back and then stick a rim around it before everything is assembled. It would make sense to me to make this rim from metal, so that it didn't have to be too thick to be string, but could also take tapped screw holes for fixing the cover on.
Generally people don't like rear covers on semi-hollow bodies unless they plan to do lots of mods to their guitars, which is a very small proportion of the people who buy them.
Last edited by Simon Barden; 29-01-2018 at 11:36 PM.