Denmark offers homeowners 20-year loans at a fixed interest rate of zero

The other is the culmination of a fifty-year process set in motion when Western economies went from gold-backed currency to fiat currency, and then from political control of currency to independent Central Banks. During this period both inflation and interest rate have moved monotonically downwards, essentially both to zero.

What if you assume that this state of affairs is strange because new, but perfectly benign, and will last indefinitely? It's absolutely true that those people who bought housing and other assets when rates were 10% have profited from a huge windfall. However, it's a one-off windfall. They simply got a discount, because 20/30/40 years ago, borrowing long term to pay cash was hugely burdensome. Today's homebuyers will buy assets at prices which reflect low interest rates, and they will pay low interest rates on their loans. As young workers, they might actually be better off in the long run. In a long term regime of zero rates, more of society's wealth is going to producers (and risk-takers), less is going to people who just hoard cash.

You might think it's nice for society to do something to correct this one-off inequality. Maybe so, but it's not fundamentally different to the other inequalities which exist. In particular, it's unclear why either artificially raising rates or artificially raising inflation are the solution. Neither of these are particularly effective in helping people who have got the short end of the stick. Both benefit some groups of rich people and some groups of poor people, and harm some other groups. There are much better solutions which can be pursued by governments directly without political interference in currencies.

Of course the type of person (job, family status, education level) who could buy a house in Berlin or London in the 1990's could not buy that same house today. You can either say 'too bad, you were out competed', or you can try to do something about it: pay teachers and social workers more, build more houses, make smaller cities more desirable to live in, provide better training and career opportunities etc. Blaming this on the dubious idea that cash in the bank should accrue 8% interest per year lets governments off the hook for actually solving the problems, and just advocates a different set of inequalities and broken incentives.

Please note that "H" stands for "harmonized", and that is one of the issues. If you change how the HICP is defined, then all the countries should produce the new indexes that should be included, with the same methodology. That is a challenge and a national political issue too in some cases.

When the bank lends you money, it usually doesn't go from its deposits. Usually, there's an offsetting loan the bank takes from other banks, at the inter-bank lending rate (e.g. Euribor). Then the bank lends you the money at, say Euribor + 1%, pocketing the difference. The funds for inter-bank lending come either by offsetting loans from the central bank, or from consumer deposits, both of which can be re-lended many times due to fractional reserve banking.

It absolutely does have to do with interest rates. Rates are kept artificially low by central banks due to all the debt that has been accumulated the last decades. We're at the end of a long-term debt cycle.

It's quite easy to see how artificially low interest rates are increasing social inequality.

Just look at house prices, the older generation who predominantly own houses have had their wealth inflated by increasing house prices and that has happened due to low rates.

Younger generations are often priced out of buying homes.

What if you assume that this state of affairs is strange because new, but perfectly benign, and will last indefinitely?

You mean this time it's different?

The current setup is not sustainable. Debt is growing faster than income/GDP all over the world (since before Covid).

In a long term regime of zero rates, more of society's wealth is going to producers (and risk-takers), less is going to people who just hoard cash.

Savings is not "hoarded cash". Saved money is usually put to productive use by banks loaning it out again to other people.

Money spent on real-estate on the other hand, is not put to productive use and does not meaningfully grow the economy.

The problem for young people wanting to but a house, at least in Sweden, isn't so much the monthly costs of paying the mortgage (which is often less than rent), but being able to put up the 15-20% 'cash' that the bank wants to see to even give you that mortgage.