I looked into implementing this at the Mosh level but it makes things a lot more complicated, plus I think Mosh is behaving the right way here.

The main issue is that the States then will control and execute the instructions, so skipping the sequences during suspend / restore would require to somehow pass that general state to the whole state of the mosh terminal. And that won't be easy. Also, I now think that Mosh should not lose its state for the clipboard.