Supply is increasing, but if that increased supply gets snatched up by investors then you haven't really increased supply for people who need a place to live.
There's no magic way around these economic laws.
Of course if demand grows faster, then prices still go up. But in absence of supply increases it'd be even worse. Supply definitely helps.
Not necessarily. By the UK Government's own estimate [1], 1-in-20 homes in West and Central London (the more expensive parts) are empty. The story I've heard is owners who use them as a store of wealth safe from their own government's hands (usually Russia, China, or places in the Middle East). They prefer not to have tenants because it adds risk and complexity. I'm not saying this is the true story, but it's what I've heard, and there are definitely lots of expensive, empty apartments.
[1] https://theconversation.com/londons-extraordinary-surplus-of...
Also I've heard about apartments and commercial rental space staying empty because people can borrow money against the 'value'. If rents drop that value shrinks. If it sits empty, no such problem. You still borrow against that commercial property that rents for $5000 a month. You were just unlucky finding a tenant the past 5 years.
But beyond that I find it's a minor problem that gets broad attention in the media. There've been lots of studies around vacancies, but they usually don't amount to anything close to the media narrative.
For example, most real estate investors discount their expected rental income by 10% for expected vacancy, because they know tenants come and go, it takes time to find/review/place new tenants, some tenants fall through, and sometimes there's a no alignment between a tenant leaving and a tenant being available on short-term. 8 or 10% is a very standard industry figure people often use for quick calculations. In the US I think the average is about 7% for example.
Now if you find that 1 in 20 homes, in a particular high-class area known for vacancy, of a particular city known for this problem discussed intensively in media/politics, are vacant... that's entirely within normal parameters. That's 5%, and supposedly it's the most incendiary piece of data they could find.
In other words, quite normal figures that have a straightforward solution (>3 or >6 month vacancy leads to hefty pentalties/fines/taxes). I'm not saying the problem is completely non-existent, but it's not that big a deal as people often think and repeat.