Seriously! When my first child was born, we stayed as long as possible, basically until the nurses more or less kicked us out. There was tons of support, and it was as pleasant an environment as I can easily imagine.
For baby #2, the focus was 100% on getting the nurse and doctor through their appointed tasks. 14 hour old baby is actively nursing? Too bad, hand her over, its time to do the measurements. We got so fed up that we requested early checkout, was told "they'll be over in 5 minutes to do last-minute checkout", and after 45 minutes of waiting, we just left.
Sometimes, I suspect "against medical advice" actually means "expected medical advice that was never actually delivered".
Pro tip for any spouses out there on that first night in the hospital:
Tell the nurses to screw off if baby and mom are doing fine.
We had a similar issue in that they would come around every hour and do 45 minutes of testing. Let mom and baby sleep and eat for a while, they've both been through a lot.
Also, for the first timer's out there: Your normal rhythm of doing something hard and then going to relax and recoup is not how babies work. Like, you go climb a mountain, take a test, have a hard day at work. Then you go home and relax and recharge, right?
That's not how a newborn works. The labor and delivery are the start of the 8-12 week long process of getting the newborn used to a day-night cycle and a feeding cycle. You really don't have any recouping or recharging time for the next 2-3 months. You don't have it after the 2-3 months either, but things get a bit calmer and you'll likely be sleeping more by then though.
I don't want to scare you off parenthood, but let you know that the normal way of things is not how your life is going to go now.
Instead of continuing to wait for the nurse doing their rounds, we went up to the nurse's station, stated our intent to leave, waived off all the "we really think you should stay", then they matched up the ID tags, cut them off, and away we went.
Yes, I have not gone AMA but I have heavily pressed a doc to get me out RIGHT AWAY because I was getting worse in a hospital rather than better. Sleep was the top concern, and my biggest frustration was how nurses and doctors would all chuckle, smile a little, and say "oh, we know, everybody has a hard time with lack of sleep here" like it's some charming quirk of the system. Often these would be like "pill at midnight, vitals check at 2am, labs at 5am, vitals again at 6am." I mean at least lump vitals together with other existing wakeups! Nurses also vary greatly, and the best ones would work out ways to improve sleep a bit and the worst were just unbearable in slavish adherence to schedules in the chart, even when some of them are obviously arbitrary or flexible. (Don't wake me up to give me a scheduled pain pill! If I'm sleeping well, I'm not in pain.)