One of the great things in 1e/2e was weapon speed/factor which was added to the initiative roll.
You and I remember those early edition combats very differently. Our group eventually ditched speed factors. We never used the weapon vs. armor charts, and I don't think Gygax actually used them either.
In those days you would decide what to do each round first, resolve initiative adding the weapon speed or spell casting time to the init roll and then do it on your turn.
This made for both a wonderfully chaotic battle and added depth to the decision making of choosing fast weapons and quick spells (which interrupt spell casting).
Which often resulted in wasted turns when the thing you decided to do at the beginning of the turn becomes irrelevant later in the round.
However in 5e there is something to be said for streamlining combat by not having to wait for everyone to decide on their action (before a round can start).
Each person resolves their turn then can sleep until their turn is up again.
Strong disagree. Players stay engaged to be aware of what's happening to their character, not just what their character is doing on their turn. Every character has a Reaction, often used for opportunity attacks, and some have special class features they can do when it's not their turn. Also, knowing what the opponents are doing helps plan your action for the next round.
And even so, how does adding in speed factors keep players from disengaging until it's their turn again? If you've got that sort of player, it just slightly moves round the point they disengage each round (assuming they're not a fighter who just swings their sword each round, so their speed factor never changes.)
You want to step player engagement up a notch? Use a "players roll all the dice" variant, so they roll to see if the bad guys hit their character, not the DM.
I certainly remember in AD&D combat was very much a "all hands on deck" scenario with people coordinating their moves.
The downside was that it didn't really account well for a changing battle.
I remember very long rounds as players, especially those with spell casters, hemmed and hawed about what to cast to minimize the chance of, again, wasting a turn or getting interrupted. And often extended group discussions about the plan/coordination of actions this round, which is not realistic in the slightest, and sometimes what a given player wanted to do go overridden by the group.
It also added another thing that had to be looked up, especially if the player was casting a spell they don't often cast. Again, the fighter and rogue, using the same weapon, already know what they're going to do for the round and their speed factor is effectively static, so they get to sit around bored while the spellcasters decide what to do.
In my experience, 5e games don't lack for co-ordination between players, anyway. If the current turn order isn't optimal for certain actions, we often ask other players to Ready an action, so someone else can do something first that benefits the Readied character or the party in general. There's also plenty of other coordination "If you do this, I can do that" scenarios beyond just someone taking a Ready action.
Do you think there is a "best of both worlds" combat sequence? If so what would it look like?
I don't. Adding in speed factors each round defeats the purpose of fixed initiative that's been with us since 3E, as the order will likely change round to round anyway. You might as well go back to rolling initiative each round, in which case you've ditched 5E initiative altogether, and not using a "best of both" mechanic.
Also, speed factors for spells were part of the balancing factor in earlier editions. The spells in 5E are already balanced against other factors. Speed factors may shift that balance in unexpected ways.
And, what about all the special actions characters can take? What about monster special actions? You'd have to assign speed factors to those as well.
I miss weapon speed. At least using a dagger had a benefit
Which is another problem with speed factors - it didn't account for reach. Sure you can get up and stab someone with a dagger repeatedly faster than they can hack you with a sword, but you have to get past the sword first. Easiest to just assume reach and speed balance each other out in that scenario and ignore it.