Valet Parking by the Half-Hour

In a hurry while taking my mom to the Heart Hospital, I decided to use valet parking. I assumed that, as is standard at restaurants, there would be a fixed charge. To my delighted surprise (given that this was to be a very short visit), the valet parking marginal price was by the half hour: $1 for the first, $.50 for the second, $1 for the third, $.50 for the fourth, etc., up to $5 maximum for any stay over 3 hours.
There was essentially no fixed price component-it was a nonlinear one-part tariff. This struck me as unusual, since the costs of valet parking the car are almost entirely fixed-putting the car away once and taking it out. I wonder why the hospital uses this pricing model? Are they trying to be nice to the many elderly, low-income patients? Are the costs somehow passed on in everyone’s medical bill?