Honestly?
Yes I do think it's a bit much for a list of rules. If someone gave me that after I came to the hospital to wish them well and congratulate them on the birth of their new bub, I'd be highly offended that they thought they needed to do that and leave my gift at the door. The birth of a new baby is a joyous occasion and people just want to shower it and you guys with love. They would rarely be purposefully inconsiderate (though i won't deny that there is a lot of "no idea-edness" happening out there )
I know there was a thread a while back about passive aggression but in situations like this I do think there are merits. There are plenty of cheerful ways to remind people to sit down while holding bub and washing your hands, in fact it's many hossy's policy.
Perhaps in regards to visitors when you announce the birth you could add a bit on the text or the phonecall "We'd love you to visit (or not) but could you give us a quick call before you pop up just in case we need some rest".