Additionally, and perhaps my biggest gripe about the system you describe, say combat just started. I rolled max for initiative, I go first. I cast fireball at the grouped up enemies and they all get hit. In the system you describe, I cast fireball at a set spot and during the animation they get to simultaneously use their move to walk out of the AoE that they WOULD have been in on PnP.
I don't know how it is in 5e as I stopped playing PnP D&D at 3.5e, but this is not true in 3.5e D&D. You can start casting your spell at your initiative point, but your spell goes off only after your spellcasting time has elapsed which, if that spellcasting time is a full round, would be at the end of the round. So your targets can in fact move out of your AoE before the spell goes off. And, that is exactly as it should be. Maybe 5e has done away with casting time for spells, in which case that would be yet another huge negative against 5e.
@etonbears, I completely agree with how you describe a good comat system for replicating tabletop gaming. If that is what was meant by a game being "turn-based" then I would be much more favorable towards it. But TB as it is generally understood is immersion-breaking and unrealistic and completely sucks.