If Amsterdam went even further and subsidized/required lenders to approve 0% down home ownership then they could likely fully solve the problem.
For rents, if 8 people want 5 units, the rent will be high enough that 3 people are priced out.
For owning, if 8 people want 5 units, the mortgage payment will be high enough that 3 people are priced out.
I fail to see any difference.
I do think that discouraging unoccupied properties is a good idea though.
Let's say 3 people are willing to pay $1500, $1600, and $1700/mo in rent. For owning, they are willing to shift an extra $1000/mo from saving in the stock market to home equity, paying $2500, $2600, $2700. There is only one house available.
For owning, the seller can charge a price where the mortgage works out to $2700/mo. The person willing to pay $2700 gets the house, and the others are priced out.
Now lets say a landlord comes in. He offers $2800/mo to buy it to rent.
The max he can rent it for is $1700/mo, so he does that. The same person gets the house, and the same people are priced out.
In every case, the price that is charged is determined by who can pay the most. Unless people are willing to pay less to own the house, I can't think of why the monthly mortgage payment would ever be lower than renting.
What a policy prohibiting renting actually seems to do, is force people to shift their (monthly) savings into real estate speculation as a condition of living there. There are some downsides to this. If the local economy is bad and you lose your job, it's likely your home value may not be good either. And people without substantial monthly savings to shift will be at a disadvantage.
The biggest argument I've seen in favor of encouraging home ownership, is that people cut back on spending in order to make their mortgage payment, and as a result save more overall (by building home equity savings instead of spending). But that's a pretty different outcome than making housing affordable.
2) On paper not a problem. There's a law against vacancy in Amsterdam, you can and should get fined. But I have my doubts about enforcements, although they have a monitoring system in place.
3) Not sure how I feel about this one, there's another argument to be made as well that rent-restrictions have a price-dampening effect and may make purchasing possible for a group who'd otherwise be forced to rent in perpetuity. Plus very low-incomes do have substantial opportunities, more than half the housing stock is social housing in Amsterdam. But agreed, this policy can be unfavourable as well, it's just not necessarily always the case.
Housing stock has to increase, rent-restrictions don't help with that. And secondly Amsterdam has to cooperate more with neighbouring municipalities and regional transport infrastructure to spread the demand around. This latter part is really difficult, but if you don't solve this problem and create ever-centralising appeal in concentrating everything in Amsterdam, you can never outbuild the demand. At some point, people must be enticed to not live in Amsterdam. That requires investments into jobs, schooling, amenities etc outside of Amsterdam, as well as good infrastructure to connect it all.
1) It doesn't solve the problem of affordable housing.
2) If the owner leaves the property vacant instead of renting, it makes the problem worse.
3) The less well off usually rent instead of buying, so prohibiting it disadvantages them.
While it's presently the trend to blame foreigners and/or investors for economic problems, I don't think this will end anywhere good.
If you have 8 households who want to live in 5 houses, there is no way to make them affordable to all 8. Full stop. Not with paying all 8 more. Not with rent controls. Not by making everyone own, or everyone rent. It's totally impossible.
The trend now seems to be that affordable housing will be allocated to a lucky few who win a government lottery. Whether this is a politically superior outcome to building more (and allowing the character of the neighborhood to change) is subjective.