AWS is perfect for large operations that value stability and elasticity over anything else.

It's very easy to just spin up a thousand extra servers for momentary demand or some new exciting project. It's also easy to locate multiple instances all over the world for low latency with your users.

If you know you're going to need a couple servers for years and have the hardware knowhow, then it's cheaper to do it yourself for sure.

It's also possible to use aws more efficiently if you know all of their services. I ran a small utils website for my friends and I on it a while ago and it was essentially free since the static files were tiny and on s3 and the backend was lambda which gives you quite a few free calls before charging.