Having managed a VPS yourself is very useful (fun, I think, and definitely educational), and takes you a long way in realizing more of what it takes to put up a website, and makes you a better developer I think.

It's not that the web apps CAN'T be run on regular hosting, but when you try and do more and more ambitious things with the sites you build, you will need/want the control (even if you scale back later when you realize you don't need it).

For example, if you wanted to try using some new database or ORM to build a project, your hosted option might not support it (yet).