Affordable small house with basement, 100m2

Is there any experience or solution in this forum regarding the quoted point that the architect earns more the more money he wastes?

The HOAI - which does not have to be applied compulsorily - basically provides that the fee is higher for a more complex project - so far, so good. And that the construction costs (namely the actual costs) are an essential benchmark for this complexity. This is unpleasant for the client. But the remedy is not complicated: one can agree with the architect on a lower basic fee and a bonus for the degree of budget compliance. As I wrote elsewhere once: an architect is not a notary. Rather, he may be open to interpreting his fee schedule only as a recommendation or guideline, and include success-related remuneration components. Budget adherence is in my view a very important client interest.

The question posed by the thread starter also interests me a lot.

Are there any solution experiences here in the forum regarding the quoted point that the architect earns more the more money he wastes? The architect is also only human; voluntary renunciation can hardly be demanded.

Your quote of the OP as well as your own statements contain the gross misconception that the architect spends the money. That is not true; only the client does that. If you want the golden faucet, get a quote for it, and commission it, yes, then the construction costs and the architect's fee, which is linked to it, increase accordingly. But it is not the architect who is undisciplined, but the client. So better take a look in the mirror.
Incidentally, the architect, of course, tracks the budget and should point out if an overrun is imminent. If the architect says €40/sqm for tiles is in the budget and you choose ones for €60, well...

The statements by surprise me a bit.
My "then" research on the HOAI topic actually showed that it is indeed applicable and binding. Fixed prices are possible according to it, but must not be below the minimum rate; otherwise, the agreement is invalid and the minimum rate must be applied! Just google it.
Edit: Just read Wikipedia on HOAI - it is a binding ordinance of the federal government that is mandatory for all activities covered by it. What possibilities do you see to circumvent this, ?

But it is not the architect who is undisciplined,

Yes and no. Some architects are dreamers and artists who don’t really care what contortions the structural engineer has to make to actually make their castles in the air buildable and the like. Also, you can literally "build in" things like overhead hours.

Regarding the HOAI: I am neither a lawyer nor any other specialist in this regulation. I also consider it practically appropriate in terms of scale and do not by any means recommend turning the architect into a discount seller. After all, there are also professional liability insurances whose coverage requires a reliable standard. In the end, I also do not want to encourage the architect to become "cheaper." That means the fee, taking into account the part of cost discipline that he can influence, should not fall below the lower benchmark. Ideally, a success-dependent remuneration component is designed so that better performance "brings" more than worse performance "harms." I have even read this basic idea of such remuneration in guides written by architects; however, I have not yet heard of any ready-made sample contracts for it. Where exactly the comma must be placed to make it compliant, I would therefore be at a loss.