You can absolutely do it all yourself. AWS simply makes it easier and manages all the services. There's no reason you can't DIY 100%. Say for instance, Linode or DigitalOcean, you could spin up and configure all the services yourself.
Although at that point, you end up spending more time configuring and managing all the services, that it can eat away at time that could be spent elsewhere. So it really comes down to what you value more --- cheaper services, or services that always work and you can focus on something else.