At some point I have run an AppService with three instances when one of them have failed. Without using an affinity cookie this then resulted in exactly every third request failing.
With the new HealthCheck feature I suppose this failing instance would eventually have been restarted, but this would still have resulted in downtime, and from our perspective it doesnt matter much if every request is failing or every third, the app is still essentially broken.
In this particular case the end result would therefore be the same with one vs more instances. Of course this case was an unplanned crash of an instance, so I suppose it may work in cases where an instance is recycled on purpose...
Iirc also the HealthCheck functionality in itself will only work if you have multiple instances, so in this cases it does make a difference at least in terms of automatic mitigation.
https://learn.microsoft.com/en-us/azure/app-service/monitor-instances-health-check