Because the part that you would use to control your extra tentacle or whatever is probably currently used for something. If you are missing an arm is obvious what part of your brain you would use, otherwise, some sacrifice probably have to happen.
Even reading, it seems, take the space that is used in people that can't read for some detailed visual processing (1).
Maybe you could add some extra processing in the extra arm, so it's more "cheap" to use.
(1) - I learnt that in "Reading in the brain" by Stanislas Dehaene.
For instance, I'm learning German and I can feel how is messing with my English, specially with the spelling (English is not my first language).
The new skill you learn may reinforce existing areas if its components are transferrable. Also, I see schemas as compression in the brain; eidetic memory shows how much some brains are capable of.
Forgetting is very good for clarification. I think your example suggests that your spelling in English hasn't been established deeply enough; I understand why you might have an adverse reaction to learning it though (German spelling is far more reasonable).
I suspect it would be possible if you can do some kind of real-time feedback/tuning of the ML model. Reinforcement learning stuff.
By slowly adjusting the model to reward hitting the ball back in pong, but also to penalize moving the real physical hand, you might achieve it.
Obviously tactile and proprioceptive feedback through the chip would enable better / quicker control, given the sufficient plasticity hypothesis.