Let's say your website requires 4 application servers, you can then tolerate a single AZ failure by using 5 application servers and spreading them among 5 AZs.
Going by your example, If your website requires 1 application server, to tolerate a single AZ failure, it requires you to double the number of application servers.
Example - we have a service that used Kafka in the affected region that went down. Our primary kafka instance (R=3) survived but this auxiliary one failed and caused downtime. There's no way around this other than doubling the cost.
*: https://commons.wikimedia.org/wiki/File:Postgresql_elephant....
For a single server deployment you can still reduce your downtime (with minimal costs) by having the ASG redeploy into another AZ on a failed health check.
