My two cents (82 pages down; probably means nothing).
Initiative and turn order is a major mechanic in D&D - even with the same spells and abilities, going to a system that doesn't use those seriously changes the game. If you want to be as close to 5e as you can, battles have to be turn-based.
Where I think the problem is in the current system is that some characters can go turn-based while others remain in 'real' time. This allows the real-time characters to interfere in combat in ways that are impossible for (and exploitative of) turn-based mechanics. When any character goes turn-based, all of them should. This can cause problems if you split the party and deliberately want to keep some out of combat because it becomes tedious to pass their turns every time they come around, but there are ways to make that easier. Like having an ''automatically end turn' toggle.