It’s true that mining is mostly done for ROI; if you can’t make a profit by running your ASIC miner, or your GPU miner, or whatever else, then you won’t run it.

That doesn’t mean, though, that Bitcoin would lose its network robustness; before BTC had any value at all, people were mining it “altruistically”, purely for the sake of adding auditing strength to the network so that they could use BTC to make transactions. The Bitcoin mainnet has far more of those plain-old CPU miner nodes than any other network, and they’d still be there even if the profit-mining operations cashed out.

On the other hand, if the ASIC and GPU mining pools “went dark”, it’d always be a worry that someone would pay to start them up again just for long enough to execute a Sybil attack. But Bitcoin has been “steered” away from such attacks before with community forks, and I doubt such a future would be any different.

If all of the ASIC mining dropped off Bitcoin would end up with a "frisbee on the roof" problem with its difficulty scaling, ie with the current difficulty there wouldn't be enough mining power left to mine enough blocks (2016) to reach the next difficulty reset in any reasonable amount of time, effectively killing Bitcoin as its transaction throughput would grind to a halt. This is an unlikely death, but still a possible one.

Why would all the ASIC mining drop off? What mechanism could cause such a thing?

More generally, a severe hashpower reduction could be problematic. An emergency hard fork to a better difficulty readjustment algorithm (like what other coins use) would solve that. Ideally that change would be made before it ended up being needed.

A huge drop in price could result in a death spiral. If the price drops such that the mining rewards no longer cover their electricity, they might shut down until the price goes back up. If enough of them do this, it could further collapse the price as the transaction rate drops.

It wouldn't need to be all of the ASIC mining, of course, just a large enough portion of it to result in massively increased block times.

Don't forget that transaction fees help to entice mining too, not just the block reward. The death spiral never happened during the frequent difficulty swaps with BCH because fees simply went up until it was profitable to mine a block -- to as much as 40% of the block reward. There's no reason in principle it couldn't go much higher if necessary.

There's a limit to how high they can go (can't offer more in transaction fees than you actually have) and even before you hit that point you may encounter the back side of Bitcoin's Laffer Curve where the expense results in lower total transaction fees per block even as individual fees rise.

It's possible that point would be far beyond any conceivable price crash, though, I don't know how to put it into anything resembling concrete numbers.