Yeah but does that really make the encounter any easier?
IMO if you get it cool but if not then it's not at all worth grinding for... that kind of thing is not gonna prevent a wipe or make your run any smoother either.
consider how this looks in Gambit.
I don't know about things being worth "grinding" for, but you should certainly be checking your gear every time you get something in the Dreaming City or Raid for enhanced gear. If you're doing your weekly bounty stuff in the dreaming city and raiding, you should have a bunch of this gear to sift through. From the sounds of things, you've probably thrown away a good number of enhanced gear.
Do I need to do anything special to get Militias Birthright besides completing the Nightfall?
Yes, go do a 100k score Nightfall clear. Equip your Nightfall emblem when you do. You get higher drop chances.
If you can, go do a 200k+ nightfall clear. Maximum drop chances. And the more people in your party doing the speed runs with 100k+ NF emblems on, the better. Best drop chances/multipler setup is with 4x people who all have 200K or better emblems equipped. Put on Genadier or Heavyweight + whatever singe and speed run it.
I personally would recommend keeping any with proximity grenades, implosion rounds, or spike grenades, then with Ambitious Assassin + Auto-Loading holster. I have several, but my Birthright with Prox + Ambitious Assassin + Auto-Loading has about 550 Crucible kills on it. I keep going back to it because Ambitious Assassin gives you 2 rounds in the mag if you get a kill then reload. Next engage is basically a guaranteed kill.
Also decent in my experience: Graverobber, Threat Detector, Rangefinder. Quickdraw is cool if you can't get an Ambitious Assassin roll.
I personally don't get much out of Rangefinder as I don't ADS with these GL's ever, but others do.