Sed, Jeez, it is hard enough getting from one suburb of a large US city to another suburb without a vehicle. Public transport is minimal and if you can find their routes and a timetable before you come, good luck! I dunno how you can be a travelling musician if you can't travel. Take a cab, an airline/Amtrack, then another cab, rent a room and you've wiped out most of the money you were gonna get from the gig.
Volunteer Folk societies are as friendly a gig as you will find, but they still expect artists to be able to find their own way to a gig. If you don't have your own PA system, the only gigs you can get are small or ones that have their own PA.
I have driven across the USA - it is huge! Forget horses, bicycling or walking! (By the time you get to the gig you are going to be really tired. Can you give your best performance when you are exhausted?) Driving is the only way you can economically do it to get you, your instruments and a PA System to a gig.
As for the Folk "Branston" idea, instead of one artist driving a couple of hundred miles to a gig where the audience has travelled less than ten miles, we'd have several thousand people driving thousands of miles to see a performer. The economics of this screw the audience. (Is this what "Country" music is about?)