Same goes for any bitwise operation <<, >>, &, |, %.

Can I write my SIMD/number abstraction and have it work?

Let's say I need rotors. With six dimensions. Can I overload it's basic numeric operations?

You need to understand that the things you want to do are the very things that others want their language to ensure cannot be done. For example, the question I'm asking is, can your preferred language ensure that operators are not overloaded? You want a language with an operator overloading feature, and I want a language with an operator-overloading-prevention feature. My preferred language lacks the feature you want, and your preferred language lacks the feature I want. The same language cannot give us both what we want, because what we want is contradictory. This is why we prefer different languages; some cater to your preferences and others to mine.