[comradelion]

It's the application that needs an OS, not the computer. It is possible (and isn't unheard of, though decreasingly common) to run software on a more featureful CPU with virtual memory and loads of RAM next door, without an OS, for example.

And it of course depends what one means by "a OS." But, generally, if you are running multiple tasks that might depend on shared resources, you might want an OS---after all, an OS is just something that mediates shared resources among different applications.

You might prefer to use a microcontroller because of power constraints, security (generally easier to mitigate physical attacks and side channels in simpler hardware), or cost and you don't need more resources.

[bongodongobob]

If you're even talking about virtual RAM, you're already in SoC territory. And the concept of an "application" on a microcontroller is foreign to me. I still don't get it.