We're playing changing initiative in our current 5e game. I'd never do it on tabletop - rerolling and rewriting the initiative table every damn round for an entire party and potentially a couple of dozen enemies/allies is just too slow and painful. But we play using FG and there's a plugin that does it automatically.
It's ... interesting. It does remove a degree of tactical thinking (or possible metagaming, depending on your point of view) since if you're later in the initiative order you can't always have your turn in the knowledge of who will have their rounds next. And as
@Reynard says, sometimes it means that your 'until start/end of your next turn' effects will only last a couple of initiative ticks (though equally often they'll last nearly two full rounds, so swings and roundabouts)
On the whole, I kinda like it. It makes combat feel a little bit more chaotic and risky, a little bit less of an optimisation problem to be solved.