Besides the busses, the deluxes (except AKL) have Monorail and/or boat service as well. Some are within walking distance to some parks.
If you're a golfer, on-site guests can make tee times 90 days in advance vs. 30 days otherwise, and get a free taxi to and from the WDW courses.
Enights, if they are being held during your stay, though it doesn't sound like your children will be up for that! However, since they are in bed by 8:00, I'm guessing they are early risers, which could make EE, especially at MK, very valuable for you.
Besides those tangibles, we enjoy the "all encompasing" vacation we get by being on-site. The outside world goes away (except for the busses and cars!). No parking worries, good service, save time, etc, etc, etc,
Now, all that said, you still might be better off staying in a 1BR offsite if its a much more affordable option than a 1BR on site (2 separate rooms in a moderate or value on site wouldn't work for you since your oldest is only 5). If you really are going to be miserable after 8pm every night, that might outweigh the other benefits.