I’ve come into this topic a bit late, but here’s my thoughts as a person who used to agree to dropped kerb applications for a local authority....
Be honest up front, a track-laying vehicle is fine provided it is road legal. If the jobs done correctly the neighbours can’t complain!
Planning application normally only required if you are on a classified road.
It’s not just a dropped kerb you get for your money, it’s also extra protection to the numerous utilities that lie just below the footway.
You will definitely need the highway authority, or it’s approved contractor to car