Most of the hardware is already there for the regenerative brakes, and it allows the driver's muscle memory with respect to braking pressure to still apply in that edge case. I'd be surprised if it were simpler to make the friction brake fallback behave identically to the regenerative system when the battery is full.
Maybe it's not worth the cost/complexity anyway, but the idea has merit somewhere in the design space.
If a Tesla would use rheostatic braking, I think it would require more cooling capacity than the cars are currently designed for. If the resistor couldn't be kept cool, then the car would have to revert back to friction brakes anyway. More cooling probably means bigger air intakes, which I think would run contrary to their aesthetic goals.
Rheostatic and friction brakes both basically convert kinetic energy into heat. Is there some fundamental reason why a resistor would be harder to cool appropriately (low thermal conductivity comes to mind, though I'm pretty sure there are high performance ceramics used for both brakes and resistors -- my heuristics aren't really good enough to make a good guess for this one)?
Well, friction brakes are cooled by the airflow in the wheel wells. Perhaps you could aircool the resistors in the same place. The friction brakes would probably still be there though; would there be space for both?
Shouldn't the resistor having to end up dissipating exactly as much heat as the friction brakes do, by conservation of energy? Is there a reason that it's inherently mechanically harder for the resistor to dissipate that heat?
Disks and pads wear out. I haven't done the math, but I assume you could put in a big (wine bottle sized?) power resistor that can take the thermal cycling more or less indefinitely.
You'd have to cool it, as other commenters have pointed out (you're putting a car's worth of kinetic energy into the thing, after all). I'm not suggesting that it's a good idea, just possible.