A couple of things need to be said here.
A wing creates it's maximum lift in total disregard to what kind of structure is behind it controlling it's pitch. And it stalls at whatever AOA it stalls at, also in total disregard to the horizontal tail's design. If the wing has slats or flaps, then they are part of the wing system and are considered, but whatever is aft on the fuselage doesn't change what the wing does, only how the entire airplane affects what the pilot will need to ask the wing to do.

The stab can't enable the wing to create more or less lift or hold any greater angle of attack before stalling.

Also, stabilators are rigged to produce forces as required by the specifications of the design envelope. All horizontal tails will stall at extreme angles of incidence and if those angles are expected in the design specs, whatever the horizontal tail design is, it's rigged to respond to keep the airplane in the design specs. Flexible camber systems like stab/elevator horizontal tails effectively change their incidence when the elevator deflects. They basically change the airfoil shape, and along with that goes their pitch. The way aerodynamic designers deal with greater required AOA from stabilators is to simply increase the available deflection As long at the stabilator deflects enough, it won't stall. In fact, the conventional tail has a limit imposed by the fixed stab (although some have trimmable ones), whereas the stabilator is limited only by the mechanics of it's pitch control system. So in fact, the stabilator system can be a lot more adaptable to envelope pushing conditions.

BTW, a very large number of model gliders are designed with stabilators and they are definitely subsonic. There are also a number of fullscale gliders that use it. And a number of private aircraft use them. They are often lighter to build, having no requirement for hinging along the span and such. They have been found quite useful by many. And the designers know that there aren't any particularly specific problems with them that occur when flaps or spoilers are used. And modelers who fly gliders have proven that over and over.

So don't worry about there being any problems specific to stabilators that aren't solved by having sufficient deflection and appropriate controls.

They work for cutting edge supersonic aircraft and for our relatively small gliders. And about everything in between. Basically, by designers who know how to employ them.