We don't need endgame for this to answer the OPs question.

There is no black and white rule for "do I have to DPS".

In every content the game has to offer and the more often you do it, you will eventually get better in it and you will eventually notice that by you getting more efficient in healing/shielding the incoming damage there will be downtimes where you are doing nothing at all.

This may vary by player and group skill etc, but once you get to this level you should try to squeez some DPS in, rather than doing nothing, amirite?