Streaks should last the entire time you are logged on (with an allowance for people like my friend who somehow just sits in orbit for 70% of his play time) and should stay up no matter what you play in between. Ohh you got absolutely blown out in crucible over and over again because team balancing is a term bungie has never heard of, so you swapped to a gambit or strike to relax then hopped back in crucible? Who cares? That should be a streak still. The whole system is anti-intuitive and anti-player. It's punishing for the sake of being punishing and trys to keep you playing a singular mode till you close the game as if that is in any way an enjoyable experience.

Throw the entire thing in the garbage and input a system where every 4th game in that played session, no matter the mode, rewards one or two more legendary gear pieces. Then players can play, are enticed to play, and it's not stupid. Then Jack up the rep across the board. Strikes, crucible, and gambit are not endgame lol, it's not like this hurts anything.