Vercel is fairly clear about where it runs your code - depending on the type of page/deployment its going to be either S3, Lambda, or a cloudflare edge worker. There is a ton of logic behind how deployments work but the general benefit of using a service like Vercel is basically exactly as described above -- you push your code and it just works and you don't worry about it.

This is an attractive prospect for a lot of folks who want to spend their time making their apps better and not building/monitoring infrastructure. However, there are some folks who really like to build and maintain their own infra and in that case a service like Vercel might not be the best fit.