[throw_a_grenade]

This is misunderstanding. There are many situations in SI where two units boil down to the same expression in terms on fundamental units, yet addition does not make physical sense.

More clear example: both Gy and Sv are J/kg (m^2 s^-2), but to add two values, one in each of those units, you need to multiply one of them by a coefficient (that coefficient depends on the kind of radiation and specific organ that absorbed this radiation). So somewhere in the math world lives a constant that is unitless 1, but x Sv/Gy, where x != 1 (again that x depends on circumstances).

Those situations just happen. It's how physics work.