It's hard to put into words what your "actual specific" role is because there's just so much you have to do. But I would say as a DPS, your job is to basically apply pressure to the healer. Somebody dies in feast when the healer cannot keep up with the damage being done or if LOS/Sleep/Stun etc is done properly. Occasionally you'll meet a healer who just drops dead and it's an easy win for you but if you're against someone who knows what they're doing, you have to know when exactly to burst to secure a kill.

As long as you know your rotation, how to burst and how much burst is needed in that moment, you'll do fine.

Also the problem with just blowing everything on the healer at the start is that they can attune (nullify all damage for 10 seconds) and they have all their CD's to top themselves and their team up. While 3 of your players is trying to kill the healer - their DPS could be on yours. At that point its about which DPS/Healer is better. WHM can just drop prism and GG you won't kill them for 30 seconds without some co-ordination.

It's always about circumstance. There's no 100% foolproof way to win. Improvisation is important but not for the sake of it. It should be calculated.

Also learn how to kite and stay in LOS of your healer. Use bind appropiately.