The problem to me isn't inviting different ages and genders, it is that when you invite them you should plan a party that will be enjoyable for all the guests.
I think that's the key.
With really little kids, family/friend parties can make a lot of sense. The kids aren't old enough for organized games, so they run around, and the adults talk and watch the kids - it's not much different from a normal get-together, there's just a cake and some presents at some point.
A kid birthday party is very different, though - you've got games and activities specifically designed for that age group, and the focus of the party is what the kids are doing. Combining that with a general party can be awkward, as in the OP, particularly for older kids and adults without kids.
The tricky thing, I think, is when the kids are old enough for a kiddy party, but not old enough to be dropped off for it. In that case, I do think it's nice to have the option to bring along siblings who are not old enough to stay home alone - it's a bit much to expect a parent to hire a babysitter for their other children so that they can escort their child to a birthday party. Then it's up to the parent and other siblings what to do.