What will happen if batteries do get overheat from such usage? What is the worst thing that will happen?
I try to avoid speculating about what the worse may be (given its rarity), but to my mind that would be "venting with flame" from failure of a defective battery. It is not common or likely, as long as you take reasonable precautions. The most important is to only use quality CR123A cells - and ensuring they are all well balanced for capacity (i.e. don't mix and match used cells, or ones from different manufacturers/batches).
Relative risk is the point. When running 4xCR123A max on heavily-driven lights, you will find that the internal battery temperature rises rapidly. Personally, I would be relucant to run any light this way longer than 5-10 mins continuously (unless it has a built-in thermal cut-off feature). I don't have any data on this, but I suspect that catastrophic failure of a defective cell is more likely to occur when placed under that kind of stress.
The other risk is to the light (i.e. excessive heat could damage the circuit or the emitter). Most lights should be designed to handle this heat, but I still prefer lights with thermal sensors to be safe (if planning to run on max on 4xCR123A for extensive periods).
2x18650 Li-ion is safer in this context, since they don't get as hot as 4xCR123A will (for the same output). The main risk with Li-ions is at the point when you are charging them. I recommend people check in with the battery experts in the batteries subforum for a greater discussion.
Again, my concern above is largely theoretical (i.e. a safe battery handling perspective). I have no data of failure rates of specific batteries or specific lights.