Mining difficulty will increase exponentially.
Only if new mining power is added exponentially. If no new mining power is added to the network the difficulty will stop rising.
The hardware necessary to mine it substantially, already costs upwards of $22,000 USD.
What are you basing this number on? What does "substantially" mean? Are you saying that only large mining rigs are profitable? I think if you buy small hardware at the right price it can be profitable too. So the amount you mine is simply proportional to the amount you invest in. Small miners can actually be more efficient because they can be cooled more easily and do not need a dedicated space.
What if the price of Bitcoin stays at around $100 ... yet the difficulty skyrockets?
Then the less efficient miners will stop mining, and the difficulty will stabilize.
The difficulty will surpass the cost of the rigs necessary to mine it.
Then no new power will be added to the network and the difficulty will stop rising. The people with the most efficient miners will continue making money the longest. If mining is unprofitable, then the network will shrink until either it is profitable, or the people mining are willing to mine at a loss. Some people who want to continue using bitcoins will mine at a loss if their business is dependent on bitcoin continuing, and some people mine at a loss just because they are true believers in bitcoins.
