Why do screws so often work even without a clearance hole? It seems like in theory, the screw should always push the joint apart (bridging). But in my experience, screws more often seem to tighten the joint. How does this work? Is it because the screw strips the threads in the first piece of wood a little bit, so it works the same as though it had a clearance hole?
I would challenge the 'usually' in your thread title, because the experience of many would suggest otherwise. But the screws you're using most and how you're using them will be factors. It may highlight the difference between power driving and hand-driven screws. And material matters, MDF and particleboard/chipboard aren't the same as wood.
So to your theory of the screw stripping the thread in the first piece of wood, my bet is that it won't be the main factor. But withdraw some screws and look. That's the best way to find out if that is what occurs.
This might not be obvious but if the two pieces are tightly together already and held that way (e.g. firmly clamped or already glued) then that spacing will be maintained as the screw is driven home. If they're not tightly together however then bridging is a virtual certainty with most screws IME — as anyone who has had this happen will have seen, as the screw is driven in it will move the first piece off the second and then the gap will not close to nothing.
Note that if using a conventional wood screw with an unthreaded portion at the top under the head and the first piece is roughly the same thickness there is no thread there to cause bridging, so that would prevent the problem since the action of the screw can overcome friction and pull the first piece down snug.