Minimum wage is $15/hr (teachers make more), daycare is open 8am-6pm. Law has 4-5 kids per teacher, so that's $1000-$1250/kid minimum, plus floating teachers (can't close a class if one teacher is sick), and there's rent and administrators. So the $2.5k/kid is reasonable given all of that - I doubt the school makes a lot of money.
To be fair, you can also get a nanny for about that (going rate is $20/hr or so) which works out with two kids.
Still though, my point is that high costs of child care in the city are a wedge that furthers the gap between rich and everyone else.