-However, my concern is that it doesn't offer a very secure base for mounting drivers or amp (ie. on subwoofers). Wood screws or threaded inserts (for machine screws) would both be better off going into ply. So, for this reason I think I would go with the MDF inner box and ply outer box.-
That's true that it's 'better' than MDF for holding in screws but in the case of subwoofers you'll find most people rec. you use T-nuts or similar Hurricane nuts and bolts into the cabinet. When you do this there's no diff. between MDF and anything and no way the bolts can 'pull out' 'cuz they're gripping the steel T-Nuts not the MDF (or plywood etc..)
FAR better too if you need to get inside the cabient ever again too 'cuz you can take the bolts out as many times as you want with no damage to anything.
I recently had to do this to my subs 'cuz I had to re-wire 'em from 4 Ohms into 16 Ohms when I added 2 more subs to my room for a 4 Ohms total at the amp (crazy I know but I already had all the stuff and still very cheap).
For speaker cabinets- say the Alphas to get back to the main topic... just painting the cutouts before you mount the drivers is usually enough to keep the drivers in place. Not that I'm saying screws aren't needed, just that I think your concern isn't needed.
I'm sure many can tell you about unscrewing a driver to take it out and finding it bonded to the cabinet and it being a real bitc- uh... real tough hehe to get out.
Of course on the planars there's no pressure of any kind on the screws and the ones GR provides (along with the woofer screws) work perfectly and look very nice.
-Also, wouldn't routed rounded over edges be more solid on ply than on MDF and not require joint putty etc to try to smooth the edges? And ply edges would not be so vulnerable to damage from knocks etc?
Plywood would be possible a little strong to guard against dings, but I think this isn't an issue for most people.
Most people don't run into their speakers too often nor bang 'em in to any walls.
Either of those would damage the surface paint or veneer you used to make the speaker look nice so plywood's not a solution to an MDF problem here.
Plywood's not going to have a perfectly smooth roundover edge either. You're going to be exposing cross-grain layers in the roundover. Could get little splintered bits, etc... No big deal, but no reason to think it'll be dead on smooth vs. MDF rounded edge IMO.
If you are using the plywood as your veneer finish you'll want to put in sepp. solid wood roundover corners to make this look good 'cuz for sure an exposed plywood roundover won't look good.
If you intend to paint both plywood or MDF will need a little prep work to assure smooth painted corners.
And actually plywood having a grain to it's whole surface will IMO be worse for painting than MDF which has a perfectly slick/smooth surface, but both can work.
IMO, just no advantage to plywood.