[nyrikki]

That is because the way you were introduced to the concepts was targeted at didactic convenience and incremental teaching curricula. Pedagogical efficiency is important but care is also needed when mapping concepts that are accepted as a priori in a specific domain to universal beliefs.

Physics uses the properties of unitful objects to help avoid errors, it is a convention and not (by itself) a fundamental truth.

If your world is physically realizable one, the benefits make this choice a no brainier, but it is still a convention with some convenient outcomes.

A unitful quantity is actually a tuple, specifically (value = quantity x unit)

In computer science and programming, assuming a priori that individual scalers are only useful in the context of units, or that they will behave in the same way can cause you real issues.

Be careful with conventions and assumptions, use them where they serve you well and avoid them where they block you from finding useful mechanical means to solve problems.