In theory, I think is a good idea. An even better benefit in my mind is that it addresses the original articles complaint by providing a form of means testing without actually means testing. The free compartment is available to everyone weather they need it or not (that is to say, weather they can demonstrate in a satisfactory manner that they need it or not), however the people that don't actually need it will self-select out.
The problem is political. At least in the US, this approach would be opposed by both major political ideologies: the right because it is a government hand out, and the left because it is unfair to have a "poor" section of the bus (see the reaction to mixed income apartments having a separate section 8 entrance, or restricting the amenities that section 8 residents are allowed to use, which is essentially what you are proposing).
Further, the nature of bureaucracies in our economics system (be they for profit or government) is to prioritize profit centers at the expense of cost centers, so it would be difficult to maintain the "poor" compartment to an adequate level. Compounding on this is the fact that the poor and homeless tend to be the least politically powerful groups, and maintaining adequete funding for this scheme would be difficult,