Is house construction financing possible at all?

Nevertheless, the obligation to make the monthly repayment already ensures an accumulation of assets, since quite a few would otherwise spend this money in other ways and NOT invest it long-term.

That is basically the essence of my "wall of text" from earlier, just written much more compactly. ☝

(...)
I doubt that a rental house causes significantly less 'work' than one you own. (which tenant would voluntarily outsource the gardener and winter service for €300 p.m. through the additional costs - few)
(...)

That is an oversimplification. The €300 "house fee" serves to build reserves for repairs and renovations that simply have to be done after a certain time. Many, if not almost all homeowners, save hardly anything and then face a broken heating system after 20, 25 years and need another loan. Or a broken roof, whatever.

In my opinion, the cold rent for a single-family house best reflects the true costs, if you subtract the 10% profit for the landlord once.
Because the landlord must necessarily build reserves from it, he must maintain the house, and he must repay the loan within a finite time. The cold rent reflects that.

Almost all homeowners hardly save anything and then after 20, 25 years face a broken heating system and need another loan.

I don't know - where does that thesis come from?
We do that, and as far as I know many others here in the forum do as well? Even in financing threads it is repeatedly discussed that there must still be enough left over for that / it has to be factored in. Surely there may be people who neglect that, but I wouldn't go along with "almost all."

You here in the forum represent only a fairly small and well-off part of all homeowners. In my circle of acquaintances, the wealth is generally not enough to manage even smaller investments like a new heating system without a loan. PS: Supporting my thesis is also the fact that a large part of homeowners cannot afford an energy-efficient renovation of their house at all. Especially not retirees.

An energy-efficient renovation is also a bit more expensive than a new heating system. Especially if you simultaneously switch from a high-temperature to a low-temperature system. For the distinction between homeowners with and without money, there was a simple proxy. Whoever sold a house in 2020 and had solar thermal installed regularly did something to the house. And whoever did not install photovoltaics at a time when feed-in tariffs were 50 cents really had no desire to take care of the house and no sense of money. Back then, photovoltaics were a safe profitable business even when financed by credit.

The 300 EUR "Hausgeld" is used to build reserves for repairs and renovations that simply have to be done after a certain period.

Only you believe that. First, a lot of money goes to common electricity + water, caretaker, administrator, elevator, compliance with various regulations that you only have in apartment buildings. Reserves are no longer such a big part.

The term "Hausgeld" is put in quotation marks because I was referring solely to the rent of a single-family house. My mother happens to own a condominium in a multi-family house, so I know quite well what it is for. There is no property manager/caretaker, no elevator either... Common electricity is just small amounts ;)