To me, the key distinction in this argument is between designated parking spaces for those with disabilities, which allow them to park closer to their destination, and the disability placards which allow their holders to park for free in metered spaces, and thus serve only as a financial subsidy to the holder of the placard. Parking spaces for the disabled near entrances make some sense. But parking permits are a peculiar way to give financial assistance to the disabled (nationally, only about one-fifth of those with disabilities are in poverty), and lead to incentives for overissuing and fraudulent use of such permits. Manville and Williams write:
"The government isn’t going to hand out free gasoline anytime soon, but at least 24 states and many local governments do distribute free parking passes, in the form of disabled placards. These placards not only grant access to spaces reserved for people with disabilities, but also let their holders park free, often for unlimited time, at any metered space. Nor are placards difficult to get. In California, for example, doctors, nurses, nurse practitioners, optometrists and chiropractors can all certify people for placards, for everything from serious permanent impairments to temporary conditions like a sprained ankle. We recommend that cities and states limit or eliminate free parking for disabled placards. We believe the payment exemption has high costs and few benefits. It harms both the transportation system and the environment, and offers little help to most people with disabilities."
A number of counts in various cities have found very high use of disability placards that allow for free parking. Manville and Williams mention a 2010 count in Oakland which found that 44% of parking spaces were filled by cars displaying a disability placard. In their own survey of 5,000 parking meters in Los Angeles, 27% were filled by cars not paying, but displaying a disability placard. Moreover, the cars with disability placards often stayed much longer than other vehicles. A 2010 study in Alexandria, Virginia, found that 90% of disability placards were being used inappropriately. In my own hometown of Minneapolis, the city council tightened up the rules on disability parking placards in 2002, when it was estimated that about half of the metered parking spots downdown every workday were occupied by cars with handicapped permits, costing the city up to $1 million in parking revenue each year.
There are some middle-ground solutions here. Donald Schoup explains one: "In 1998, Arlington [Virginia] removed the exemption for placards and posted "All May Park, All Must Pay" on every meter pole. Because it is easier to pull into and out of the end space on a block, Arlington puts meters reserved for drivers with disabilities at many of these end spaces. The purpose is to provide parking in convenient locations for people with disabilities, not to offer a subsidy that invites gross abuse. Cities can reserve the most accessible meter spaces for disabled placard holders, but accessible is not the same as free." Another proposal is that if those who are disabled need more time while parking, they can have cards that allow them to stay longer at a given spot--but still to pay for the full parking time they use. Instead of free parking, collect the revenue and use it to give those with disabilities taxi vouchers or other transit services.
From a 2012 research paper by Manville and Williams in the Journal of Planning Education and Research, here's a list of the states that have free parking for those with disability permits. The list does not include municipal-level rules: for example, New York City offers free parking to those with disability permits, but the state of New York does not. Anyway, here's their list.