The real barrier to entry is the point between "cheap" and "free"--especially when first learning. For me, that was when I was 10/11. No chance of getting hold of a credit card to get a "cheap web host or VPS." I could only experiment with what my computer was willing to do on its own.
Heroku's almost the right thing for this, I think, though it still requires a credit card to sign up fully (it doesn't technically, but it does to enable free add-ons, so without a credit card you don't get, say, database persistence.) Obviously, Heroku is geared for adult developers--or, more specifically, to start-ups that Heroku hopes will become monsters dependent on Heroku's stack.
What would be perfect is a service like Heroku, but specifically for people learning to code; maybe something joined-at-the-hip with an online coding-school website. When you attend a real CS program, you get access to the labs and mainframes to test your programs on--where's the online version of that?
So, anything like this already exist? Or should I build it?