The "right to travel" does not imply that a particular MODE of travel is guaranteed to you.
Do I have a (nonrevokable) right to use the public roads to walk or to cycle? Why?
Do I have a (nonrevokable) right to use the public property in a reasonable manner? Why?
PS 'nonrevokable' means: may not be arbritrarily revoked.
Are you conceding the the state may arbritrarily deny Drivers Licenses since driving is a privilege?
You have a right to walk, but you do not have a right to wear shoes.
Or access to taxpayer built and maintained public roads.