Yes, you're right with your first point, and I had considered the fact that landlords will most likely pass on any more modest tax on to the tenant. That's why we need a more radical solution. Rent controls/caps being a first step, perhaps.
I disagree with the second and think that there should be limits on how much housing an individual or company can stockpile.
Everything you can think of has an unintended consequence.
Rent caps - landlords sell en masse, house prices crash and with it the economy, government has to step in.
More tax on landlords - just gets passed down to tenants.
Subsidies - cocks up just about everything it touches.
Controls on landlords - alienates higher risk tenants and forces them into the hands of unscrupulous landlords who don't follow the rules.
I think the two big fixes are an extreme tax on foreign property ownership and penalties for empty houses. Taxing only foreign ownership doesn't pass the cost on to tenants because most of the market doesn't have to bear it and empty houses/holiday lets are mostly outside what is meant by private rentals. But mostly not do what the government is always best at, pulling the ladder up. Penalise the people who have already done it not the ones still trying to do it.
Why are they? And to what end? How many private rented homes should there be?
I believe zero. I realise that’s unrealistic. But I also can’t see an argument for anyone having a portfolio of properties.
What circumstances can you outline to support a huge private rental market?
Asking in good faith.
Unless the government builds a few million council houses (where, how are they paid for, what happens to property prices and by extension UK economy) then they fill a need. People must live somewhere and not everybody can buy/wants to buy. If you kill the private rental market there is nowhere for them to go and what does remain multiplies in price.
If you argue that nobody should have more than one house and therefore there is enough to go around, then you can blame the government for that one not being viable. When Gordon Brown screwed private pensions people turned to buy to lets to supplement the inadequate state pension. Get rid of that and the government is going to have to pay for all those people's retirements or risk losing 3 million votes.