No, the companies and their employees would NOT win more if it were public. Want to have a semi-confidential conversation? Better be on the private bus. Want to have the bus have wifi VPN'd back to the home office? Works better on a private bus. Want more certainty of finding a seat, or having a power outlet to charge your laptop? Works better on a private coach. Want special hours to accommodate a hackathon, or a holiday party or other special event? Works better for a private service. Want to keep protesters from annoying your employees...?

It's not the case that everyone would win more, IMO.