For me static combat with the same initiative each round and without combatants jockeying of advantage over each other in terms of order of events is not as dynamic and fun or strategic. It is not like this stuff come up all the time, but often enough to want to play around with it. Like all house rules. . . heck, like all rules! . . if they are unforeseen consequences we'll deal with them when and if they come up.
Sure, dynamic combat over static is highly preferable.
But for me, the delay action is just too pat. It's basically pick any initiative under yours and act then - no cost to doing so, other then acting later. Ready action, on the other hand, imposes a cost - your reaction AND it sticks a concentration requirement onto any spells you want to cast as a reaction.
So you can still jockey around with the ready action, but since there's a cost - more math to weigh.
An example, that's niche but certainly comes up often enough:
My caster PC goes right before the baddie and wants to cast hold monster on it (let's assume no legendary resistance etc. for the moment), I want the rest of the party to get some serious shots in on this thing! If I cast Hold Monster on my initiative, the baddie gets a save, if it fails great BUT it then goes and while it can't act it gets another save before anyone else can act.
I decide to gamble, I'll let it act once AND THEN cast hold person.
With DELAY (as done in 3e but for 5e) this is trivial, I position myself right after it and go. I get my full set of bonus, action, movement and I get to keep my reaction for stuff like counterspell etc.
With READY it's easy but riskier. I state my trigger (something like "I cast once the baddie has finished all of it's actions) I ONLY get my action so if the baddie moved out of range of my spell - too bad (unlike Delay where I may be able to compensate). Also I had to start casting on my actual initiative so if the baddie (or something I wasn't anticipating) hits me before the trigger - I may well lose my spell. Also if something happens before my next turn (on it's standard initiative) no shield, absorb elements etc. This is a significantly bigger gamble than just simply delaying!
I suppose I prefer option 2 because it provides options, but at a cost PLUS it doesn't mess with the actual initiative order (I was never a fan of how much the 3e initiative order jumped around YMMV).