As a person that has been of both sides of this discussion i have only one rule: If you want to speed through the strike, fine but stay alive. That's what i do when i speed rush a strike. I stay alive and by the time the other 2 guys catch up, the forced checkpoint its almost cleared and we can move on fast to the next checkpoint or the boss. You want to kill everything in the strike, be my guest, i'll wait for you at the boss, which is the only place where the non existent catalyst could drop. Long story short, you play your way, i"ll play my way. Easy.