In that regard your argument is a little like saying kids test question such as "Jennifer has 3 apples and gives one to Bob and Terry, how many does she have left" isn't decimal because the calculation is written in English rather than as a "number sentence" (as schools call them). But clearly the kids are still thinking about those numbers as decimal even if the question is not phrased as a mathematical equation.
Whereas some other cultures used base-12 or base-60 (https://en.wikipedia.org/wiki/Sexagesimal) which, incidentally, are also believed to originate from finger counting much like base-10 was.
I believe the Romans also thought about things in decimal despite their numerals being logarithmic. However their numerals do follow the decimal orders of magnitude.
The reason being is because decimal is the base system people learn when growing up. It's also widely speculated that one of the origins of decimal is around the number of digits (it's not an accident I've chosen that ambiguous term) on our hands: 10 fingers and thumbs. You might mentally map that to number line when trying to assess the distance between numbers or visualise formula but ultimately these would be mental models you generate on top of decimal rather than in place of.
They are integers with a fixed point, which is an entirely different domain.
edit: you've now edited your post to repeat a lot of what I put above. Though I doubt intentional (probably a race condition of us both posting at the same time). Anyhow, I'll keep what I posted as it's still relevant.
It is true that in home shopping lists there aren’t prices. I was thinking more about company ones (like parts).