Is a ventilation system cost-effective? Does it save money?

In most cases it does not save money, or where it might even be financially profitable, there are very likely other options with a much greater leverage. However, the gain in comfort is as high as, say, with a dishwasher, which most likely does not save money either (of course it depends on user behavior, but the same goes for a ventilation system), yet most people who own one do not want to be without it anymore. Of course, you can wash by hand, there are many who voluntarily do without a dishwasher, but those who have one would (my personal estimate) probably buy one again 90% of the time, if it is affordable.

In most cases, it does not save money, or where it might even be financially viable, there are very likely other options with a much greater leverage.
However, the gain in comfort is as high as, let’s say with a dishwasher,

A dishwasher can be retrofitted at any time without having to "temporarily tear up" the floor coverings and underfloor heating (punctuation emoticons are sorely missed at times). For this reason, the retrofit option "decentralized" mainly exists – whereby "decentralized" is also synonymous with "not networked" (all inefficient small-scale systems) and expensive because it is virtually an anti-synergy effect: imagine an internal combustion engine with a battery, a starter, and a catalytic converter for each cylinder. In new construction, a decentralized controlled residential ventilation would either be 1. a great solution for the use case where only a few rooms are to be equipped with it or 2. (as the majority or continuous equipment) a fool’s game, which in my opinion no one practices except the supplier "Kern". For a granny flat, a decentralized controlled residential ventilation can also be economical even in new construction.

Yes, important note. My analogy referred solely to the aspect that a technical installation can "pay off" on more than just the economic level. That is already the case - quite soberly considered, in most cases already when building the house itself.

Yes, important note. My analogy referred solely to the aspect that a technical installation can "pay off" on more than just the economic level.

And my addition points out that even with image cropping, the economic aspect goes beyond the worst case of "simply not worth it." If I have a used car with crank windows and want electric windows, I can remove the cranks and install little motor boxes – not fancy, but no drama. If my house does not have controlled residential ventilation and I want to retrofit it "comprehensively," it's practically a gut renovation, which depending on the construction/modernization year is economic madness. A dishwasher can be installed in a (base) cabinet compartment, often even reusing the door as a front panel.

Hmm, I don't see it quite that critically. You can also accommodate that later with flat ducts in a suspended ceiling. If you don't start off with only 2.25m clear room height (that would indeed be a planning error), that would work without problems. Nevertheless, I agree with the basic statement that if you want to achieve the last 10-20% beyond Pareto, it is always cheaper at the beginning of a project than at the end (excluding inventions of miracle technology in the meantime).

The gain in comfort is, however, as high as, let's say with a dishwasher,

I think that's a nice comparison. Both are machines that take something off your hands that is actually easy and in most cases quick to do yourself. This gain in comfort is then diminished by the fact that the devices require regular attention and maintenance and have to be replaced after more or fewer years. By the way, I don't have either of the two machines - even though I really don't mind technical devices. They just haven't appealed to me.