I think this is a brilliant idea. I also think it would probably be considered illegal in most parts of U.S. now.

Taxis are licensed and regulated. "Jitney cabs," while efficient and potentially providing a great service to low income people in lower density areas, are generally illegal. Your idea would probably be illegal under the same laws that ban jitneys, though you are proposing something that would be a giant leap forward over any jitney system.

Which US states have made hitch-hiking illegal? | Answerbag.com

In North America hitchhiking is forbidden in some areas, such as near prisons. In some cases, a local government, such as New York City[1] where hitchhiking is widely considered very dangerous, may ban it altogether. Certain US states have created conditional bans, such as Utah, Pennsylvania, New Jersey and Nevada; it is frequently illegal on the actual shoulder of Interstate highways, but is usually legal from highway on-ramps. Nevada, for instance, bans hitchhiking, or signaling for a ride, altogether, but walking on rural interstates is permitted. The same law applies in Wyoming. On the other hand, the state of Oregon (with the exception of counties in the tri-met bus system--Clackamas, Multnomah, and Washington) permits the freedom of hitchhiking as well as walking right on the Interstate. Oklahoma, for instance only expressly bans pedestrians and hikers on tolled interstates-the free ones are 'ok', provided one is in a safe area for cars to briefly pull over. Many Canadian highways similarly have hitchhiking bans.

Areas which do not permit pedestrian traffic (such as limited-access highways) are typically by implication off-limits to hitchhikers, even in the absence of laws directly addressing hitchhiking itself. Roads and their segments signed or otherwise designated as no-stopping zones are also de facto prohibiting hitchhiking since vehicles cannot legally stop to pick up hitchhikers, even if pedestrians are not prohibited.

This list is far from complete, Washington state also banned hitchhikers (on the Interstates, and elsewhere?) in the wake of the Home of the Green River Killer's activities. We've quite a series of legal hurdles to overcome in the states.

In addition to resistance from cab/MT companies, consider that of the automotive sales/maintenance industry, and of fuel retailers. As irrational as it may seem now. Of course this would be swept aside in a real crisis situation, but never underestimate institutionalized greed.

Like your plan nonetheless.