For me, 2 of the BEST perks that come with staying onsite are the ones nobody seems to mention!
1) ROOM CHARGE! It is so, so much easier to charge everything to the room key. Food, souveniers, snacks, rain ponchos, you name it. If they sell it on proprty, I can probably charge it to my room key! That way, I can go to my hotel's front desk and pay off my current charges every few days, and I only have a few transactions hitting my bank account. Is much easier to balance my check book, and when I check out, I get a detailed list of everywhere I spent my money - from a balancing and budgeting perspective, this is awesome to me. It also feel safer and more secure than carrying around and pulling out large sums of cash, or my credit cards. If I lose me key to the world card, guest services can deactivate the old one and give me a new one, and nobody else has my credit card number! That extra layer of safety and security PLUS convenience is my NUMBER ONE deciding factor when debating staying off site. For me, it is very important.
2) Hand in hand, is package delivery. I don't know about you, but I've seen things I really wanted to get in the parks, and really don't want to carry and keep track of a bag full of stuff all day, and I may be too tired to go back for it at the end of the day - with a child, I imagine this would be even more of a concern. If I buy something almost anywhere onsite (in the parks, Downtown Disney Stores, etc) I can fill out a form and pick it up the next day (or 2 if it's the purchase was the end of teh day sometimes) at the gift shop in my own hotel.
Transportion can be hit and miss, as others have said. But charging to my KTTW card and picking up my purchases AT my hotel are 2 major perks in my opinion, and are worth it for us.