As others have said its mainly due to kids carrying all sorts of bugs on them and trying to keep the ward in order. When my dad was in having treatment for cancer (in Sheffield) my sister couldn't take her kids in to see him even though they'd come all the way up from Cornwall!! Granted he had no immune system but sometimes its just not worth the risk.
Mrs Skip was in a while back having a lumber puncture when mum, dad, grandad and 2 kids came in to see grandma in the next bed. Nurse was straight in to get rid of the kids and 1 adult. The last thing our lass needed was 2 kids next door to her saying "whats this? whats that do? Can we go yet?"
Its not only your family on the ward but other peoples and some may need more rest. Do the video thing, he'll be able to watch in more than once and may mean more to him knowing the trouble you've all gone too.