If you're in a single AZ you're not in multiple AZ. Migrating between AZs isn't multi-zone either. Running at 130% capacity in three AZs, that is multi-AZ (to us, in our availability configuration). If an AZ goes down (which in some regions we use has happend 0 times) we lose about 30% capacity, but since that's our margin of scaling anyway we can keep going as-is, even if there was no 15% additional capacity available in the remaining AZs.
Some sort of manual active-standby configuration really doesn't require AWS or a Cloud, that stuff is the same 90's implementation it has always been and practically boils down to attaching your RAID1 USB HDDs from one PC to another PC and booting that bad boy up as 'failover'. (yes, that's an example, and yes it's an extreme one)
If you have capacity planning, and you plan accordingly, you take service provider limits into account, just like you would with anything else. Having two power feeds into a distribution warehouse doesn't help much if neither can't handle 100% of the load in an industrial park. So while having two feeds might seem 'redundant' to a single tenant or customer, it's only really redundant if either can supply all the demand of all connected customers.
The same applies to fiber connections, plenty of fake-redundant connections that are suggested by customers to be 'redundant' turn out to end up at the same PoP and if the PoP goes down your redundant fibers are worthless. In the same logistics distribution scenario, your trucks can't deliver goods if the destination warehouse itself is offline, and now you need redundant warehouses.
That's obviously a weird thing to do at smaller scales, but the fact remains that AWS having an AZ go down is only a small piece of the puzzle, and only really a problem if you didn't plan for it appropriately.