For two of my births I left within two hours. I got up had a shower had something to eat and hi ho see ya later.
That was in NZ though where I had my own midwife for pregnancy and for six weeks after birth. So I knew I could call on her at anytime if I needed and she would come. As it was she called in on her way home from the hospital later that night just to check we were all settled.

With my my two born here however we have had some complications during labour so although I wanted to go home from the delivery suite I wasnt allowed to. I left fairly early the next day though.

If you feel good and confident with loads of support then there is no reason you cant go home soon after.
There is nothing like been home in your own bed with your brand new baby