Hello, I am the reporter of these car parks. I think that no one should be a judge of the utility of a tag compared to an other. As already said, a car park is a land use, like the others. And I think that emergency vehicles aren't real users of openstreetmap (it would be very dangerous!!). So I think that speaking of deletion is not fair.

For the real issue of the public or private use of the car park, if you think that it would be valuable to add this information, you can check this page : https://www.aigle.ch/N344/parkings.html and report the informations. However, be careful to use the proper attribute : in most of cases, only parking is restricted, and it is allowed to go through the car parks to foot and reach pedestrian ways (see for example https://www.google.ch/maps/@46.3219804,6.9581597,3a,73.2y,220.38h,99.2t/data=!3m6!1e1!3m4!1sHGzXCdWfYzupJHVP0pdSJg!2e0!7i13312!8i6656 )

Cheers