Everyone has different experiences with the game. On average, doing a strike will yield me on average at least 4 blue engrams plus whatever the rewards are at the end. Maybe this has to do with luck, or maybe it's just that I literally always have the most kills of the fireteam. I do very well in strikes, they are good to me. You might be able to find out just how proficient I am doing strikes somewhere in my stats.
I really can't say that strikes give more engrams than loot cave because like I said, I don't have the patience to do that and so I can't give any credible comparison between the two. But this was never even my issue with OP. My problem is that when you are doing a strike and you decide to go ahead of everyone else and you die in a respawn restriced zone, it screws your team mates over who actually like clearing a section of the strike of enemies before moving on to the next. Why? Because if you are the only one who dies in a RR zone, then the other people also die and are then spawned in the RR zone, locked away from previous sections.
I agree about the cryptarch. And personally, I have way too many legendaries and exotics than I can even use at the moment, so engrams aren't even a priority for me anymore. I would happily pay $5 for an additional 20 inventory slots in my vault. Really, I don't care about engrams at this point.
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Yeah I'd be willing to pay for more slots too.. I have 3 Titans and even I am running out of space.