New Years eve is a midnight thing and the parks stay open after midnight. The crowds are so large for it that parks could go into phased closing and often do.. Even if you take off after the fireworks at midnight, you will take 2-3 hours to get back to your room unless you can walk there but first you need to get out of the park to start your walk there and it's as packed as it can be on NYE. Figure most people will not get to bed until 2-3 am at the earliest and they aren't going to make an early morning rope drop since many of them just don't stay up that late and didn't expect it to take 2-3 hours to get back to the room.
Epcot is the drinking the new year in place to be so those participants that decided to include alcohol and lots of it in their evening may not even see a park on sunday but it helps a lot of people just not make it to the parks until the afternoon.
I personally think it's one of the best days to rope drop magic kingdom if you are up to it. Most went in for NYE or the day before as MK does it 2 nights in a row so they aren't looking to do MK again and everyone else is still asleep and being lazy from their after midnight adventure the night before.
It will steadily grow but it'll be that odd 1 day where it's crowded but not ludicrous crowded.
EDITED TO ADD: this is not counting all the other just NYE things disney has to offer. Contemporary, hollywood star wars desert party with nye theme, atlantic dance hall, various restaurants with something special liek a nye watch the fireworks from here theme. there is just a lot of options to be out until the middle of the night and that is what NYE basically is. people just aren't awake or as coherent the next day unless you plan your nye around being able to get out of the resort early.