It should be possible for the jammer to subtract off its own signal rather more effectively than anything which doesn't have access to the pRNG it uses to generate the interference.
The thing is, GPS signals are really weak at the receiver. They're technically below the noise floor, and receivers have to use shenanigans to get a usable signal at all. If you're transmitting the jamming signal, you're really close to it, and therefore it is really strong near your receiver. I wouldn't like to calculate how many orders of magnitude stronger than the real GPS signal, but it would be a lot. Generally, subtraction works when the two signals are similar in strength, and you still lose definition in the received signal. GPS signals are so on the borderline of being able to be received that this would just not work at all.
> They're technically below the noise floor, and receivers have to use shenanigans to get a usable signal at all.