"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)."

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.