I am in favour, for the reasons listed by Beswitched.
A number of villages around me are full of holiday homes, which means that they are full of tourists in the summer, and deserted in the winter, when the residents have no amenities to keep them going. It becomes a vicious circle when people are priced out to second home buyers, so the school has fewer pupils and closes. Families with young children move out, so there is no need for the mother and baby group, and so on. The same happens with the WI, reading groups and similar social arrangements, as well as the GP and other facilities mentioned above. Even the pub stops being a local as it is full of strangers for most of the year.
I think that the owners who rent the houses out as businesses pay reduced council tax, so the council has less money coming in for local amenities, which also happens where I live (a small town) with the Air B&Bs that have sprung up everywhere. I hope that they are targeted too, if this spreads from Wales to England.