Another aspect to consider is the likely effect it would have on difficulty. Along with the new algorithm, it would almost certainly involve having to implement emergency difficulty adjustments to the code so that blocks don't come to a temporary standstill when the hashrate suddenly plummets. Also, since Bitcoin uses the total cumulative proof of work as part of its consensus mechanism, we should keep in mind the possibility it would make future contentious hardforks easier to pull off.
Bitcoin currently attracts both the largest accumulated proof of work and the largest economic majority. All the myriad forks we've witnessed so far haven't been able to keep pace with the proof of work Bitcoin has accumulated, but that wouldn't be the case if those who disagreed with the new algorithm continued to support using ASICs. The new algo would almost inevitably be the minority chain in terms of hashpower, so supporters of the new algo would have to fall back on purely the "economic majority" argument and would also have to be pretty damn sure they'd win that argument. Quite the gamble.
CPU mining might suffer from the same problems, and on top of that the network will be at the risk of attacks from botnets
And just to
stress that point a little more... Not exactly something we'd want to encourage in Bitcoin.
Yep, it would be similar to how when BCash forked they had to do some nasty trick with the estimated difficult arguments involving a series of forks... not cool for Bitcoin. An altcoin can pull that circus off but Bitcoin is too serious to go along with that.
Also the BCash side will for sure try to profit from the chaotic period to pump and probably deploy a spam attack while things are attempting to get solved).
Simply put, it's too late for Bitcoin to change PoW. We will need to see some kind of disaster that incentives global consensus to change it, and even then it will create conspiracy theories around the fact and there may not be global consensus even there.