I'm a bit baffled by this actually, maybe it's because my dd was an only one for nearly 5 years but I and her friends' mums were always trying to get 'playdates' (we NEVER called them that 7-10 years ago!) organised, as it was so much easier to entertain two children than one. Sometimes we (mums) stayed as we became friends, sometimes we would do each other favours looking after other dc so someone could work/go to an appointment etc, but I have never 'dreaded' or 'hated' having friends round.
My best friend and I were also neighbours (our gardens met at right-angles at the top) and we spent every available minute round at each other's houses, gardens, playing out on bikes, roller skates, etc - I can't imagine how dull my childhood would have been otherwise! (I also have only one sibling, 6 years younger, so we never played together)
From the age of about 4 it is fine to leave your child at a friend's house, and probably does them good. I wouldn't want someone's dad who I don't know hanging about my house, I would just say, it's fine, you can go!
I know some children are a nightmare, and you might want to limit engagements with those children, but find some nice ones fgs! Anyway, t is worth a bit of hassle to have that blissful time when they are invited back...
I do allow Wii but not for the whole time, as they tend to interact a lot and be physically active. I don't allow telly though, generally, as that is something they can do on their own. I think that is a waste of having company.