Plug compatibility removes a major problem, but having a compatible plug does not mean there is a mechanism in place to identify the individual non-Tesla vehicle such that they can have the power turned on and be charged correctly. Much more would need to be done to make that work. Other charging providers often require a card of some type and Tesla doesn't have that capability.
At least with recent enough versions of the protocol, CCS supports card-free authentication. This is starting to be rolled out, at least in Europe; see, for instance, this announcement from Fastned. I'm pretty sure I heard that Electrify America is planning to introduce this support in America, too. Going the other way, I have no idea if Tesla is using this exact same mechanism on its European CCS-equipped Superchargers. If they are, then it should be trivial for them to enable non-Tesla vehicles that support this standard to charge at Superchargers. If Tesla is using some non-standard authentication method, OTOH, then all bets are off -- it might not be hard to implement this system, or it might be quite tricky. Also, I don't know what cars currently on the road support this new standard, so it might currently be quite limited. OTOH, most new cars going forward will support it.
Another issue with non-Teslas charging at Superchargers is cable length. Most CCS and CHAdeMO chargers come with longer cables than Tesla uses. If Tesla were to open up its Superchargers in Europe, they might be usable by some cars, but many would have their charge ports located too far from the Supercharger to reach; or they might be able to plug in only when parked in a way that blocks two stalls. Thus, extension cables would be necessary for at least some cars; or Tesla would have to install longer cables.
Speaking of which, my understanding is that extension cables and adapters are explicitly forbidden by the original CCS specification. I've heard that this prohibition is being relaxed for the newer CCS specifications, but for now, that's a roadblock for a CCS adapter for Teslas. (I'm not an expert, though, so I'm foggy on the details, and may even be completely wrong.) Presumably the prototype CCS adapter for European Tesla Model S/X is being designed and built around the updated standard with fewer prohibitions on adapters.