For us it's that relaxation factor. When you stay on site at Disney everything, yes everything is taken care for you. It's SO convenient. We've been on family vacations but Disney is the first place that I've felt totally relaxed after I get there. Like another poster said once you pass through the welcoming Disney gates the rest of the world just fades away with all it's worries.
I remember in 2003 strolling along the walkway in front of the Yacht Club and Beach Club across from the Boardwalk on a warm June summer night with my DW and DS3 and everyone was just relaxed. Even the people we passed and walked with. I remember commenting to my wife how relaxed and nice everyone was. Everyone was just having fun. To me seeing smiles all over, people being genuinely nice, holding doors and being considerate of others was totally part of the magic. This was after having a great day in the parks and coming back for a nice swim in the afternoon..... ah just thinking about it is making me breath easier.
Compare that to staying at the parks all day because you can't leave to go to your off site hotel, trying to find your car in a super crowded parking lot. The stress of loading everyone up. Dealing with overtired kids who wanted to pack the summer into one day at a Disney park. The stress of driving in and out of Disney with the 1000's of other drivers and finding your offsite hotel.
Compare wanting to watch the awesome nightly fireworks display when you're standing there in super tired feet surrounded by 1000's of people in the park to relaxing at your resort on the beach or in your room/balcony watching these same awesome fireworks.
I also remember the atmosphere not just at the resorts but all around. The Disney music always remindes me as a child (in Canada) on Sunday night TV watching the "The Wonderful World of Disney". It was really cool for my DS3 to wake up and have breakfast or later dinner with a Disney character.
Also to remember the detail that Disney puts in it's parks in terms of landscaping and great looking architecture? The same holds true as to what you see at Disney Resort outside the parks (at the Disney resorts and outside the Disney resorts). Being offsite you don't get to see this at all. For example the Epcot, Boardwalk area is beautiful. The Boardwalk has an atmosphere of a 1930's Atlantic coastal village and it looks like you've actually transported to the 1930's
In 2000 we stayed off site at a nice resort, the Embassy Suites Lake Buena Vista. In fact we really liked the Embassy Suites. On that same trip we split it with a few nights at the Contemporary. Wow what a difference, the convenience, the monorail and the relaxation. In 2003 we stayed at the Swan and it was fantastic and has been our best family vacation. Never again will we stay off site.
Hope this gives you a feeling of "Wow it would be cool to stay on site".
Andy
DONT HAVE TO LOOK AT MY CAR AGAIN 
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