Currently, we can either select all channels("Copy entire document") or select the channels one by one manually, each and every time we use this function.

Suggest adding two new options:
1, Copy Animated Channels
2, Remember Current Selections
The first option will copy only the animated channels.
The second one will remember current selections (whether they're selected manually or by checking those options), and automatically keep them selected next time using the function.
So that every time we animate a cycle, and need to copy the first frame to the end frame, we just need to click "OK"(with above two new options checked). It's much more handy than selecting the same channels one by one, and time by time manually.