There are mechanical reasons in the 5e system why actual changes in initiative order once it has been established do not exist and are not permitted. There are ways that it can be abused and broken unfairly, due to the way other skills and abilities are designed to work.
If you want one quick example, take this one:
Party of four are fighting a villain who is a high level monk and several minions. Monk rolls top of initiative, party members are after her, minions are all below the party.
Monk uses extra attack and flurry to bop each character once, applying stunning strike to all of them. Normally, this would mean the players would be stunned for their turns, but by the time their turns came around a second time they'd all be free to act, unless the monk wanted to burn the resources to pull that same trick again, and they may not have that many ki points.
Monk has had her turn,
Players skip theirs, functionally,
Minions get one turn to move up and attempt to subdue the players uncontested.
Monk's tturn would be next - DM says "Actually, the Monk chooses to delay her turn until later in the initiative order. She's going to go after her minions now."
- Players, who should have recovered by now, are *Still Stunned* - because the monk has not taken her turn, and the monk having her turn is the timing for when the stun ends.
- Minions get a second turn to attack the stunned players for free.
The villian has just gotten a second full turn out of one application of stunning strike, without having to spend any additional resources at all, and has saved five ki points and risk of saves... all for no cost, just because she 'decided' to move herself further down the turn order.
Moving yourself in the turn order doesn't gel with the way 5e is designed - we have the Ready action instead, and it is written in a way to avoid these kinds of abuses, specifically.
I will note that I disagree MOST strongly with forcing casters to concentrate on their readied actions - it's not a fair stricture, for a number of reasons. A caster should not have to dismiss their wall of force just to 'be ready' to huck a firebolt at the first guard who runs around the corner. That's dumb.
