The problem is a lot of the places people have second homes are rural/coastal.
These places do not have hospital capacities like city hospitals.
They don't have the housing and population density, either. Unless half of London suddenly started camping on the beach or taking holiday lets the difference would be negligable.
My second home was lived in permanently by a family before it became a holiday home, as were most people's, I imagine. If your second home is a normal residential property with council tax payable on it then it should be taken it into account when providing hospitals and other public services. The fact that your second home may sit empty for a few weeks or months at a time is not the point - they don't know when or how often you are, or are not there. If you sold your holiday home tomorrow to a family who wanted to live in it full time, or you chose to move in full time, it wouldn't automatically make the hospital any bigger or better equipped, would it? You'd re-register with a local GP but that would be it.
Part of the reason Covid 19 is spreading so rapidly is because people in cities cannot physically get enough space between them to stop the spread. Look at the photos of the underground when those people were still being made to go to work. It was like shooting fish in a barrel.
If had managed to get to my holiday home before lockdown in that country meaning that i could not easily get there, I'd have spent the time gardening in the fresh air and I'd not have seen a soul except for a weekly supermarket visit in a small town. As it is, I can't even go for a walk in my city without having to duck and dive and to avoid the hordes. Social distancing is virtually impossible in certain circumstances.
There are not enough of us second home owners to make any real negative impact on quieter communities, however. Most of the peak period crowds in holiday areas come from short term holiday lets, not second home owners.