honestly the only thing i've found since 2e to speed up games is a trick one of my old DM's used. 2 min hourglass. He'd tell us to roll initiative, start going around the table. number one what do you do. if they couldn't decide in 2 min, they went to the bottom of the round and next guy up. If they couldn't decide the second time around in 2 min they lost thier combat round. It is amazing how much this speeds up any edition.
For, say, a four person party, that’s up to 8 minutes per round. Plus the time it takes to resolve all of those actions. Plus all of the NPC actions. That does not sound like a quick combat to me. In any edition.
Nevermind that some players simply will not be put on a clock like that. Or will not be able to think past their stress if they are. In my experience, timers actually make analysis paralysis
worse. Although, admittedly, I’ve never tried it with such a generous limit.
The main slow-down of combat is the character sheet. In olden days, most of what you wanted to do (if you weren’t a spell-caster) came out of your imagination and built upon a few pretty basic abilities.
Nowadays (and, really, since Skills & Powers/Combat & Tactics), players are encouraged to find their answers on the character sheet. That takes time. They must decide between options. That takes time. They must be filled in on what they missed because they were scanning their character sheets and trying to decide between options. That takes time.
Frankly, that’s not going away without a major overhaul. But here’s an easy thing that does speed things up (through a general streamlining and by encouraging players to pay attention):
Opposed initiative checks. And only when it’s relevant.
Combatants do what they’re going to do and if the timing of it conflicts with someone else’s thing, the dice decide which happens first. It’s simple. And it works. (Also, it’s less predictable than cyclical initiative, but that’s an unrelated bonus.)