These limits seem weird to me. CPU is a compressible resource. You can get by with less, and it's OK to temporarily soak up available surplus. Memory is incompressible. Either you can allocate it or you can't. It's not OK to "burst" in terms of space because you can't take memory away from a process. It has to give it up freely.

So these are two completely unalike resources that should be treated very differently. A process routinely overusing CPU can simply be capped to a certain rate (I assume you can do this on Windows) but a process that grows too large should simply crash. It doesn't make any sense to take down an application for an hour because it used to much memory.

I suspect that the reason for this enforcement is that Azure has taken some liberties with the isolation between sites and they can't figure out how to charge resources properly. But that is their problem and it shouldn't leak out through the interface and harm the customer.

Yes, it's common but handled a little more idiomatically, by presenting your available resources as VM/instance/machine. Of course, you aren't given the ability to exceed those metrics in a traditional cloud environment.