The problem with changing how initiative is determined is it creates entirely new incentives for certain kinds of fleets. Deciding it based on number of ships (lowest chooses) might create some other unforseen circumstances such as giving preferential treatment to fleets focusing on larger ships to the exclusion of smaller ships (which already had been a problem in my local meta after wave 2 hit, although it seems to be restabilizing). I'm not necessarily opposed to discussion on the subject, but it seems unlikely FFG would change such a fundamental aspect of the pre-game.
If we were redoing Armada from the ground up (with a time machine!), I think an alternating first player system (I'm first, then you're first, etc.) might help with some of these problems but you'd need an entirely different way of doing objectives. I don't think that kind of change given the game state right now would work whatsoever, though.
Wouldn't this actually make the triple tap worse? If you are second player with Demo and can definitely ensure last activation and then go first the next turn?
It would but only on segments where you're 2/1. On alternating 1/2 segments it makes it much basically impossible to pull off. It's imperfect, of course, but so are most suggestions for changes here.
If you wanted to make it iffier, opponents could roll/flip for first each turn, but you'll have games being decided by whether the coin/dice gods favored that one specific roll on a crucial turn. People don't tend to like that.