I'm not sure if anybody anywhere ever played completely true to that flowchart.
And they sure as hell didn't do it twice.
Close proximity can still mean standing behind a
meat shield front-liner.
In your circle of gamers, perhaps. Not here...

We've used individual initiatives since forever - each participant in the combat gets a separate initiative for each thing they're able to do in a round (thus for example if you're a Fighter with 2 attacks per round, each attack gets its own init.). We use (usually unmodified) d6s, and players just leave the dice on the board in front of them until the action represented by that dice has been dealt with. Simultaneity* is not only possible, it's ever-present: when 15 things are trying to happen in a 6-segment round, there's going to be overlap!
* - this bugs me immensely about 3e-4e-5e initiatives, that the strict turn order makes it so things can't happen at the same time.
IME, and this seems consistent with what others did from what I've read here, Weapon Speed and Weapon-vs-Armour-Type were not commonly used.
If PCs in your games were casting those multi-round high-level spells in the field you lot got to way higher levels than we ever have.

That said, most multi-round spells aren't intended for combat use anyway - they're either divinations (e.g. Identify, Augury, etc.), curatives (e.g. Cure Disease), or special-use spells e.g. to banish a demon you've already got restrained.
A lot of spells take a full round to cast, but that's about the longest casting time we ever see in combat.