Second homes and vacation homes should be unaffordable. They are a luxury.
Taxes that are too high transition the outcome from wealth redistribution to punishment.
As for the comment about kings and lords, I suppose you're not familiar with the story of Robinhood...
I’m British, I think our society is better than the US due to things like social services, the NHS, etc. What is being discussed here is way outside the realm of British (and definitely American) way of taxation and public/social services.
You have to look at the intention of the tax - as per this discussion - is not about wealth distribution but about enforcing a policy by trying to free up existing homes for the homeless.
In the advocates ideal position there would almost never be any money collected from this tax because it would make a second home or holiday home unaffordable. If people truly want the homeless to all be homed then why not use tax money to build more homes in better locations for those that need them? In the US, UK, and most other countries there is massive amounts of available real estate (could be via building up or building out). The issue here is more than finding a house. Who is going to pay the power, water, rates, insurance, furnishings, transport costs etc (those Martha Vineyard homes are not a great location for homeless trying to work).