Sure – you can set up a couple of VPSs running MySQL, then set up a durable, replicated configuration. Then you need some system to spin up new instances when an instance fails. Then you need some kind of UI to allow that to happen. And you need to implement some kind of point-in-time recovery system, as well as backups, user authentication, monitoring… and so on.
The point is, AWS allows you to buy those services instead of spending time building them yourself. There's nothing wrong with building your own database cluster if it makes sense for your use case – but there's nothing wrong with buying one in if it makes sense, either!
Sure – you can set up a couple of VPSs running MySQL, then set up a durable, replicated configuration. Then you need some system to spin up new instances when an instance fails. Then you need some kind of UI to allow that to happen. And you need to implement some kind of point-in-time recovery system, as well as backups, user authentication, monitoring… and so on.
The point is, AWS allows you to buy those services instead of spending time building them yourself. There's nothing wrong with building your own database cluster if it makes sense for your use case – but there's nothing wrong with buying one in if it makes sense, either!