I like the idea of split side initiative (I believe that's what its called)
Basically everyone rolls initiative independently (though monsters are grouped together) and anyone who goes higher than the enemy is "group A", while anyone who goes after the enemy is "group B".
Every round is group A, enemy, group B.
I think it does a good job of merging the strengths of group initiative with the strengths of individual initiative.
That is what I use in D&D, typically. It has the immense advantage in 3E through 5E that the Dex mod, individual initiative modifier still matters. And of course, each player making one roll before each round is not nearly as cumbersome as the GM making a lot of rolls. The DC that the players need is set by the main monster init mod + base of 10.
As far as handling time goes, I measured it carefully. In 3E, when switching from book initiative to this style, I got combat down to taking on average about 40% of the book time, at least with 7+ players. (I didn't play enough with 4-5 players to get useful data.)
For my own system I use a variation on that idea that has Fast/Middle/Slow slots for initiative, with players rolling to see which slot they are in (based on the DC). Monsters can be in any slot, but always go after the players in a given slot: That is, fast players, fast monsters, middle players, middle monsters, etc. I only roll for a few of the monsters, typically, with the rest defaulting to Middle.
I'm not too worried about the details, actually. I merely reverse-engineer the initiative process to be easy to do, likely to clump small groups together, but still allow some variation round to round. My own system is still in play testing. I think when I get into some of the bigger fights, I'm going to break it down further into Fast Melee/ Fast Ranged / Fast Move & Act, and so forth. The idea is that anyone doing one simple thing in the phase goes first, then ranged attacks, then everyone else. Then again, that might be overly detailed for what I'm trying to achieve.