So the price settles at the cost of electricity.
Then they reduce the number of coins per block. So suddenly it comes even less worth it to mine. Until the value of each bitcoin rises to match, causing people to want to mine again.
If the value of each bitcoin did not rise, no one at all would mine and the network would grind to a halt (no confirmed transactions).
Unless they have a mechanism to reduce the difficulty factor at that point. I'm not sure on that point.
This isn't true. The system has several modes of adjustment and it will always be worth it for someone to generate blocks. If the value of a coin didn't rise to match generation costs, people /should/ stop mining -- but those that remain will collect more coins or transaction fees as the difficulty drops to compensate. Overall the economy as a whole shrinks, but never grinds to a halt.
That is still enough computing power to make the network moderately secure.
Entities with a vested interest in Bitcoin being unhackable by those with too much CPU power might then run non-profitable mining setups.
More likely the inefficient miners will be forced to quit mining as they will not be able to compete with those who either don't pay for power, or are not a commercial endeavor that is doing so at a larger scale.
Whether that is two months or four years away, who knows.