I hate the Delay action, 'surprise rounds' and misuse of the ready action and wouldnt play in a game with any of them.
That's just me though. It's one of my pet peeves. They're efforts to fix a problem that doesnt actually exist.
I allowed readying outside of combat at first, because it made sense to me. But then, as the players kept jockeying for ways to take advantage of ready, the monsters began to do the same thing, and this whole "ready action minigame" started, as the savvier players would put more thought into their triggers (and reap better benefits), the less savvy would not do so well, and it got to the point that players were readying actions to counter possible readied actions of their enemies...
And I realized this whole mess needed to go.
As for the "delay/hold" action, there's a specific reason the 5e team did away with it, and would rather you use ready instead. Ready requires forethought and has a cost (in that you can't take your whole turn in reaction to something happening on the battlefield).
"But James", I hear a figment of my imagination ask, "what if I want to go later in the turn? Why should rolling high on the initiative be a penalty to me?". To which I remind you, early in turn 1 is early in turn 2, which is after everyone acts in turn 1. To be able to precisely time your turn "ok, the Cleric will act right after the Dragon attacks to heal the party before the Dragonrider acts" is a huge advantage and more than the game system intends you to have.
Of course, I'm certain that any DM who allows these things in their game has thought through the consequences and can deal with it. But it was making too many headaches for me and my group.