Powershell can't handle ctrl+v either. It puts in a ^V character. You can paste with a right click in Powershell, but no ctrl+v.

Not out of the box, but ctrl+v works with https://github.com/lzybkr/PSReadLine

"Powershell ISE" does

ISE isn't really a terminal emulator though. It's an IDE.

Why would I need an additional shell app to be able to simply use ctrl+v? For instance, on OS X I use the default terminal shipped with the OS, it does everything I need for a terminal application. Is a pasting functionality consistent with the rest of the OS too much to ask for a default shell?

That's a fair point. powershell ships by default though, it should be the default instead of cmd.exe