That's the whole issue you don't seem to get. As OKW you are so bound to your battle-group headquarter that you are on cold turkey once its gone.
Just because I say you should get a battlegroup eventually doesn't mean that you can't survive without it. Why wouldn't you eventually get it when the game automatically shits a halftrack onto the field for you to build one? (And it's relatively cheap and offers useful units.) I regularly go mech --> panzer --> battlegroup.
Medkit strats are perfectly viable, one of the benefits to mechanized is you have significantly more munitions income than you normally do if you're micromanaging it.
I think it'd be more viable if it didn't require vet, but I don't think it needs massive changes.