Unmanned stores in the Amazon Go mould are already switching from turnstiles to airlock-style entryways; these can easily recognize and deny shoplifters access. (Never mind that these stores also usually have some form of positive identification, e.g. a card tap or hand-print scan being required to enter; so it’d really just be a matter of blacklisting the account associated with your credential.)
There’s no reason that manned stores couldn’t adopt these more-strict entry access systems as well; manned stores just haven’t invested in such technology yet, because they don’t need it in the way unmanned stores do (where an unmanned store without an entry-access system could literally experience 100% “shrinkage”, if someone decided to back a truck up and start loading.)
Alternately, the facial recognition could just trigger a phonecall; which, combined with a simple policy that any car belonging to a shoplifter has no right to park in the lot, would mean that such cars would have a tow called on them the second the shoplifter gets out of their car and walks into view of a camera. This wouldn’t work in most of the world, but in the car-centered US, I could see it being a very effective deterrent.