More likely healers don't have mounts because, until this expansion there was rarely a shortage of them. Now that they introduced a fourth tanking job with a rotation that's, honestly, more interesting than tanking jobs have historically been, and now that they made stance dancing go away for tanks, people have been more interested in playing the job. But before that, Square was doing anything it could think of to get people to just play tank at all. If healers do indeed get an overhaul next expansion with another job option, the shortage of healers in the wild will likely go away, and the need to provide incentive to play the role will go away with it.
Also to the original point, mounts don't really do much to incentivize people to play the role, just look at how often PF groups go up to farm an easy fight with 8 tanks just so people can get their mounts... would be the same thing if they added healer mounts.