I've reopened this (rather than creating a new topic) because there is a case where this feature would be useful and pressing C doesn't cut it: If you want to copy/paste in the same place between two different levels. This could be useful in the case of repeats, or Part I / Part II levels, when a terrain change is needed to one version to fix a backroute, and you want the other versions to have an identical layout.
You can of course do this by hand (by editing the text files), or by taking note of the position then moving the pasted pieces to that position, but those do feel like extra steps that shouldn't be needed. And in the former case, some users do not feel comfortable editing the files by hand.
And while writing this, I thought of another edge case: If you want to cut pieces to work on stuff behind them or whatever, then paste them back when you're done. (Though counterargument: Relying on the clipboard for this is very risky, and should maybe be discouraged.)