It’ll hold ok without the glue. The glue is there to keep the wood bits in place the next time the screw is removed...
Good point. Yes, the toothpicks will probably fall out when you remove the screw, but if you dab them in a
little wood glue first, then that won't happen.
I know I said not to use epoxy+drilling, because adding anything too hard to move out of the way of the screw is a recipe for damage, but if you put the screw in while the glue is wet, then you avoid that risk. The problem is squeeze-out. Epoxy is hard to clean up, polyurethane glue is a downright nightmare, and even wood glue is a problem if the squeeze-out ends up hidden under your hinge. You really don't want to be ripping off chunks of wood or finish when you lift the hinge at a later time.
So, if you do glue, the safe thing to do is use so little that none ever leaves the hole.
All the toothpick and dowel methods should work fine for one of the hinge holes but if you run into something that needs more strength or if you need to have a more finished appearance then do what I recently did on a mahogany door for a nice curio cabinet repair. Drill out the stripped hole with a sharp brad point bit so it will have sharp neat edges. There are tapered plug cutters of different sizes. Cut some plugs from a piece of the same type wood and glue that in the hole matching the same grain direction, finish the same to match and drill a new hole. The advantage of these plugs is that the screw will be engaged in edge grain not end grain like it would with a dowel or toothpick which will hold up much better in the long run.
That is admittedly overkill for a cabinet hinge hole but hopefully might prove useful for someone with a more demanding repair.
I remember a kit sold at my lumberyard that had a conical drill bit and a bag of matched conical plugs (think pencil point taper). You drill/ream out your hole, glue in your plug, but it flush and now have a do-over.
It's probably a great solution for re-centering a poorly positioned screw hole, but its way overkill for one that's just loose.
Plug cutters have a very shallow taper that's almost cylindrical. Yes, for severe damage, that's sometimes the best option. I usually use a forstner for the hole.