An 8 month old is hardly a guest. He or she would not even eat anything.
I think if you invite parents of children, you should expect the family to come to the wedding, I mean...really...why would you just invite the adults? I think weddings are a FAMILY event. I would never have a wedding and expect my guests not to bring their children, it is a family celebration.
The problem lies in these weddings with over 200 guests. That is your problem for having such an enormous wedding for sake of gifts and money, not for the sake of celebration of love and family. If you don't know them well enough to have their children present, then you must not know them enough to really care deeply on a personal level that they are at your wedding. (They meaning parents.)
Inviting guests that you do not know is not o.k. with me. I do think single people should be allowed to bring a date with them. You would never invite half of a married couple and who is to say their guest is "flavor" of the week?
When you put such tight restrictions on guests, you run the risk (especially parents) of having them choose between their children and getting babysitter which BTW...in this economy...how can people afford? (Just taking that perspective since that has been thrown out there for wedding sake) and not having the guest come to your wedding.
Call me crazy but the reason I invited people to my wedding was because I care about them and they are a part of my LIFE. Not just a name on a guest list.