Keep in mind your family is just now getting into the teen years. Right now you all travel to and from the parks together. As the kids get older, some might want to sleep late, or stay in the parks late, or ride TOT for the 50th time. Onsite buses mean they can do those things.
I'm not sure if this is enough of an advantage against saving money or a larger space. Just something else to think about.
We recently returned from a trip offsite (Wyndham Bonnet Creek) where our older girls stayed behind at MK a few times and we picked them up later. It was very easy to do. We had them walk over to the Contemporary after MK and we picked them up there.
It's true that this is an advantage of staying on-site. However ... we mostly always stayed off-site for all our trips prior to this year. Two weeks at a time, either trading in timeshare or renting locally for ~$1400 for the two weeks. When we were there in 2013, we bought DVC, enough points to give us the same experience as our off-site trips = two-bedroom villa for two weeks every other year. Ignoring the initial buy-in, our maintenance fees on those points over two years are about $4K. If you don't want to pop back later to pick people up, your kids can take a LOT of cab rides for $2600.
Other aspects may still make on-site worth it to some people (and we, after all, did buy DVC), but I find most logistical issues like this one that arise from staying off-site can be resolved with an application of cash much less than the difference in cost.
I have only stayed onsite once in 2010 and honestly I couldn't wait to leave. I felt like a prisoner. Others don't feel that way, I know. That's way i started and ended with the disclaimer that I am only talking about what worked for me.
I know exactly what you mean. I think this may depend on location though; when we traded from RCI into Boardwalk in 2011 it was so annoying to get to our car that I felt exactly this way. On our first DVC stay this summer we were in different resorts and I didn't feel it as much, especially since our kids were older and easier to get to the car with.
One aspect to this that I think is important though is the answer to the question: If you are staying on-site, do you remain on-site at all times or do you enjoy going off-site? We like to go off-site to take advantage of cheap[er] groceries to stock our fridge with, restaurants that don't need ADRs, etc. even when we stayed on-site.
One thing I would also comment is that of course everyone's mileage may vary, but in general the timeshares / rented homes that we stayed in off-site had more square footage for the same descriptor (2 bedroom, 1.5 ba or whatever) than the villas we stayed in at Disney. The living rooms were bigger. If you're just a family of four that likes to have separate bedroom and living spaces, then this might not matter so much, but for a family of 6 it will be noticeable when everyone is hanging out before dinner or whatever in the common space.