Time is supposed to be more or less flowing in combat, happening in a sort of simultaneity that is abstracted for functionality. If characters can delay their turns, then they can order themselves exactly as they want to in the initiative, which will cause them to inevitably group all together in the exact order and optimum rhythm they desire, every single combat, every time, without variation. At this point, initiative itself has become redundant and has no purpose to existing at all. Being able to delay your turns would make combat even more formulaic and boring than it already is.
Being able to wholesale delay your turn also has substantial ramifications for spell and ability abuse, many of which revolve around the timing of turns, which being able to slide your turn down the order past other enemies destroys the balance of.
In 5e, there exists the Ready action, which is limited and does not actually shift your turn in the initiative, and this is for very good reason.
I'm in support of 5e's ready action being properly implemented.... but that would also recall a proper implementation of reactions, so...
