I think you are confusing delay and ready.
Nope.
Delay does not supersede someone else's actions. You have to declare a ready action to do that. Delay just lets you drop your initiative number.
Maybe you misinterpreted what I wrote. I am in total agreement with what you wrote here. Mechanically, you are correct.
It doesn't let you compress time any more than acting on your normal initiative count did. You are just doing what you normally would have done, just on a lower initiative count.
If you view it mechanically as just an initiative number, then your POV is easy to understand. If you view Delay as a mechanism where a PC can instantly react to any situation in the encounter, then you can understand how implausible and cheesy, and potentially powerful Delay can be.
The player of a PC who is not delaying cannot instantly react until his initiative. A lot of things can happen until that time.
The player of a PC who is delaying can act and react whenever he wants to. He cannot interrupt anyone else's turn, but he can act on the very next turn if he wants. It's not a very plausible state of events from the PC's perspective.
Don't view it mechanically like you are playing a game of Monopoly (i.e. don't view it from the player's POV), view it from the perspective of the PCs.
Example:
Player of PC Cleric: "I delay".
NPC 1 knocks Fighter unconscious.
Before NPC 2 whose turn comes up immediately after NPC 1 can coup de grace the fighter, the Cleric steps in.
Cleric heals fighter.
Coup De Grace can no longer be done.
NPC 2's turn.
Delay can be used to prevent a PC death in this example. What a player uses Delay for is irrelevant, it's still this supernatural ability to force your PC's (or NPC's) actions in at any time before the next creature's turn and the ability to react to the most recent set of events. It's totally game mechanics driven and implausible, hence, cheesy. It doesn't make logical sense.
The Cleric PC isn't preparing an action like with Ready (which makes sense, "when an ally falls, I cast cure wounds", the cleric is prepping a specific action). The player of the Cleric is reacting to NPC 1's turn before NPC 2 gets to act. If NPC 1 had cast Hold Person on the fighter instead of knocking him unconscious, the Cleric PC can cast Dispel Magic instead of Cure Wounds.
I might not be describing the issue well here, but this is what I dislike about the Delay action. It's totally metagamey.