I suppose the difference there is that by and large people who find the new tax too onerous can reduce their cigarette consumption or even stop smoking altogether, but people can't just stop renting their home.
well yes, but you're still allowing cheap second house, but not third. This means more middle class people can buy an investment home, but they will have to stop there, discouraging landlords with a huge stock of houses. You don't want to discourage investment in houses, just oligopolies/monopolies on the housing stock, and also unoccupied houses.