Do I need to keep the Ascension expansion boxes as I have the original one?
It looks like that version of Ascension has the Broken Token Box Organizer (or similar) included, which should allow for most, if not all, of the expansions to fit into the one box.

The game normally comes with an insert that looks a little different.

As such you would not need to keep the additional expansion boxes if you have no desire to resell the game, or display the boxes.