Still need to synchronise data, update DNS records, wait for TTLs to expire.

HA architectures exist for a reason because that last step is a massive headache.

They need to do fire drills and practice this maybe daily or at least weekly? Failover being a normal case. Can’t you do failovers in DNS?

A significant percentage of users will still have their DNS resolver chain caching the old host.

Because TTLs are a guide not mandatory. And many companies/ISPs ignore it for cost reasons.

Yes, you can do it in DNS. Update the record with your new ingress, then wait for the timeout on the old record to assert itself and the new connections move over.

Not all DNS servers properly observe caching timeouts, so some customers may experience longer delays before they see it working again.