Dear Rational,
There is logic to madness – even (or especially) “frum” madness, aka “krum”.
I heard the logic of someone illegally parking (blocking a driveway etc) when attending davening in shul: Davening is an “essay” (a positive commandment) and illegal parking is (at best) a “lo sa’asay” (a negative prohibition), and we all know that “essay docheh lo sa’assay” (a positive commandment overrides a negative prohibition)!
So yes, a choleh is a “cheftza shel mitzva” and like the hoshana we must klup him 5 times on the ground till we fulfill the mitzva.
Besides, when we visit we remove 1/60 of his illness, so our visit benefits the choleh more than rest or convenience.
For a choleh, there is leniency on a shvus (d’rabbonon) on shabbos….ask yourself, what is more important, a shvus or a hospital rule?! If a shvus can be ignored for a choleh, kal v’chomer a hospital rule about bikur cholim zmanim!