Hi Feathers, I think you need that "on". You can't "walk a road", "drive a road", etc., I think. But you can drive/walk/etc. 10 miles, a short distance, etc.
Thanks Kooyeen. I feel inclined to agree with you, after repeating those sentences many times, but walk and drive can take a pseudo-object, as in the following sentences:
# I drive this road every day.
# It is tiresome to walk the same road every day.
That's why I wonder if it's okay to omit on... I appreciate any input