I know this process can be quite slow, but on a long enough time frame it's conceivable there may be no net loss and possibly even a gain global reef acreage?
But coral is built to respond gradually over decades. It's never going to be able to migrate in time at this rate.
1. Temperatures drop.
2. Temperature variability increases. (Seasons are more meaningful away from the equator.)
The second issue, of temperature variability, is a main problem that prevents reefs from migrating away from the equator in response to global warming. The corals can't tolerate a wide range of temperatures.
The other problem, as you say, is the time frame. Reefs are built up over thousands of years, and we are warming and acidifying the oceans over mere decades.
(And ocean acidification isn't helped at all by moving away from the equator.)
Coral reef ecosystems take centuries to establish themselves and mature. They can't simply grow legs and walk a couple miles north every year.
What "really bad things" would you or your children suffer, should all the corals suddenly become sentient and beam into outer space? Just curious.
"Well don't worry, we'll just get food from somewhere else" is not a real answer. At some point, life on a dead planet just isn't worth it anymore.
We are looking at the devastation of an entire habitat. Many species that rely on that habitat may cease to exist. As a consequence, many species that eat animals from that habitat may disappear too.
Worst-case, we're faced with the disappearance of an entire food chain. And since many large ocean species travel the entire world, the consequences will not remain local.