What are the game playing impacts of allowing players to take turns out of initiative order? [duplicate]

As per a previous question I asked RAW do not allow players to go later in initiative order in 5E as they could in earlier editions of DnD and other roleplaying systems.

What are the potential things to consider if I choose to home brew changes to this behavior as part of my own rules?

The rule I am considering is as follows.

In a players turn they may either hold an action based on a trigger as per RAW or they can choose to delay there entire turn until after another stated players turn. A player may only delay once per round and cannot name a player Or NPC higher in initiative order to wait for. E G a 5 character combat 4 players and NPC roll initiative and are in order players 1 to 4(high to low) with the NPC sitting after player 3

Player 1 can choose to delay their turn and take it after players 2-4, or the NPC, they state they will go after player 3

On player 3 go they may choose to either go after player 4 or now, they cannot decide to go directly after player 1

Player 1 now takes their turn and must have a turn they may not choose to delay again.

Next round the players return to original initiative order.

In order to stick to stack guidelines I am looking for specific examples from players and GMs who have tried this rather then opinions.