I appreciate your being such a good devil's advocate, however as ForkMeOnTinder points out, there is already the super complicated[0] overloaded O(N^1.58+) operator for arbitrary precision integer multiplication, easily argued to be vanishingly less useful than simple vector operators, particularly if they were well-expressed at the IR level and well-mapped to modern hardware / instructions.

The ask isn't for general operator overloading (I'm also in favour of not having that), rather just not stopping native algebraic type support at scalars; the C function atan2(y, x) basically just wants to give you the complex argument, for example. Really it would just do so much to unify and simplify everything, besides being able to write vector stuff in a sane way; if every rando has to write their own vector and complex number classes, I'm much less likely to vouch for its correctness.

[0] I've recently been looking into Karatsuba multiplication to reduce it from O(N^2) to O(N^1.58): https://en.wikipedia.org/wiki/Karatsuba_algorithm