I am of the opinion that dice- or card-based initatives are not good systems (nor is resolving fire simultaneously), but I also consider that you can't have a truly good, headache-inducing wargame with more than two players. (Because, to me, a good wargame should be giving you a headache in decision making - dice rolls are very much a secondary concern, you should be spending at least as long deciding what to do (because the decisions should be hard, because that's the fun) as you do actually rolling dice).)
The reason I don't like those systems is that random initiative and simultaenous fire takes away one of the most cricually important set of decisions in a game, i.e. the decision about what you are going to sacrifice, because you if you act here first, the other guy will act THERE first and something is going to get screwed. That, to me, is among the single most important parts of playing a wargame, more than the shooting, certainly more than the dice rolling (I really don't care for randomisation at all beyond the bare minimum required to task resolution generation and if you can replace it with decision making, all the better), more than the models, more than winning or losing (I don't play competation, ever) or anything else - it must present difficult tactical decisions to be made.
A wargame that doesn't have that sort of decision making, where there often is NO right answer, only a set of trade-offs, doesn't stimulate me. I don't particularly care for "challenge" in any other avenue of gaming (e.g. on computer games, where I quite happily never go above normal if you can even get me off easy and have to problem with using the optimum builds) - but TT gaming the the one and only place I demand it, when I'm playing an actual person.
Now the trouble with that is, for a lot of people in my experience, is that they really don't want that sort of game (the rules don't tell you how to win, and a bad general can't rely on good dice to make them not a bad general); some folk just want to have a more social sort of game, roll some dice and move their models (which they likely have painted to a far better standard than I do!) around, or as Full Thrust once put it, more of a six-pack-and-boldy-go and explictly not have to think that hard about it. Or they simply can't play that sort of game; if you can only play at conventions once or twice a year, you can't play enough to get a grasp of that sort of thing. (Obviously, at the moment, the vast majority if us can't pay anything at ALL, certainly in the UK.)
But even that said, I still think BT would benefit a lot more from an initiative system whereby you pick a unit, activate it, move/shoot etc, then the other guy does, until they've all gone (akin to HBS BT). It would make the game flow better, even if it did not speed it up a little bit. (How you determine who goes first could be done a number of ways, including randomisation). (While you could do everyone moves before everyone fires, I think that is better left to games where there is more or less no terrain (like starship or fighter games) where relative position is pretty much the most important thing; on the ground, terrain is the great leveller.)
Failing that, and perhaps especially with large numbers of players, using a cyclic initative system (ala D&D 3.5/PF1/4E/5E), whereby you roll at the start and from then run in sequence would be one other solution.
I would, incidently, and totally agnostically to the discussion of what to change, suggest doing what I've been doing and half-inching HBS BT's evade chevons idea; instead of trying to remember how far that mech moved (especially on a big game and seperate move/fire phases) and thus what its TN modifier is, have little tokens (I literally pinched the evade chevons) you just plonk down with your mech after movement, equal in number to the TN modifier, which should likely smooth things along as well. (Granted, if playing on a map sheet, you might have to plop them on the record sheet instead, but non-map games it makes it visible for everyone.)
