Required build height is 12mm, but the desired vinyl has only 4.5mm thickness

Compensation compound is precisely made for that. Why should one avoid it?

Leveling compound is precisely meant for that purpose. Why should one avoid it?

Because then in the kitchen only vinyl can be laid in the future. Tiles, laminate, and parquet are practically out of the question because the leveling compound would have to be removed again (with a lot of mess).

OK to answer the questions:

Why exactly should it be this vinyl flooring?

Have you ever gone choosing floor coverings with your wife/girlfriend (or both at the same time )? I think that answers the question

Leveling compound is made specifically for that. Why should one avoid it?

As already said, immense effort, so that in the end the raw floors of this floor do not lie on the same level anymore and you are forever stuck with 4? No.
The possibility number 3 mentioned by nordanney is probably the most acceptable variant.

Why did I even ask this question here in the forum? Well, I had hoped that someone would say "yes, your problem is a common question, there is the following product xyz with which you can arbitrarily increase the build height". Apparently not, but the thread still helped me. =)

You simply don't use 4mm vinyl. It prevents you from switching to other types of flooring.

Because then only vinyl can be installed in the kitchen in the future.

I don't see that as a problem. You can't plan for 30 years of changing tastes...

I didn't think nordanney's option 2 was that bad either.

We have a new building and still decided to live with the small step. It doesn't bother us at all, and we have all floor coverings open as an option for the future. We looked at the 7mm on the tape measure and decided that it's not that bad at all.