No one will forbid you from walking -- no Disney police will pick you up and no one will force you onto busses. But there are no walkways, sidewalks or safe walking areas between most of the resorts and parks. There are no other ways into DAK from the "outside" other than to go through the parking toll booths, so you'll be walking through those too, which have no sidewalks or walking areas and are 8-10 lanes of cars. The road shoulders between ASM and DAK are grassy, swampy, and muddy. Cars regularly get stuck in them when they try to cut through. There's very little shoulder there -- not much gravel or anything like that to walk on -- and cars are zipping past you at 55mph. Also ... once you get through the toll booth at whichever park you're at, you've got another mile (at least) of parking lot to walk through.
If you're choosing walking instead of bus because you think it will save time, it won't. If you're choosing it for the exercise value ... trust me, you'll get enough exercise walking around the parks. Take the bus!