I've been naively setting up our distributed databases in separate AZs for a couple years now, paying, sometimes, thousands of dollars per month in data replication bandwidth egress fees. As far as I can remember I've never never seen an AZ go down, and the only region that has gone down has been us-east-1.
There was an AZ outage in Oregon a couple months back. You should definitely go multi AZ without hesitation for production workloads for systems that should be highly available. You can easily lose a system permanently in a single AZ setup if it’s not ephemeral.