Glad to know there is a pattern here, and it makes sense once spotted. I have put in a feature request to enable double key rate in other files:
case=142129
and we are already considering adding the paste menu to other files:
case=17417
for now, you might want to try Windows built in clipboard history in these other files, Windows Key + V. It's not the same as VA's paste menu, but it can come in handy at times.