Karl-
You bring up an interesting issue, it really is almost unfair to take away the key resources to the AI, as they are so terrible at doing without it, or even getting it back. The AI has clearly not been scripted well enough to deal with this situation. In fact, it almost a "cheat" the AI is so bad in this area.
There is no question that denying the AI rubber with just a small defensive force (including building a city on it so that you are not constantly at war) is game over for them.
Maybe I should just play with my own "house rules" that I can not take their resources away. Or.... maybe I just need to play at a higher level (I play on Monarch, probably need to play Emperor).
No matter how far behind in Monarch, once I get Infantry and sit on all the rubber, the game is just a matter of turns (sometime a lot of turns) before the AI is wiped out.
As MadScot discusses, there probably should be an equivalent unit for each main unit that does not need any (or a different) resource but would have worse statistics. That is an interesting idea.