Pemdas and bodmas are not bullshit, they are a standard to disambiguate expression communication. They are order of operations. Multiplication and division are not on the same level, they are distinct operations which form the identity when combined with a multiplication.

Similarly, log(x) and e^x are not the same operation, but form identity when composited.

Formulations of division in algebra allow it to be at the same priority as multiplication by restructuring it as multiplication, but that requires formulating the expression a particular way. The ÷ operator however is strictly division. That's its purpose. It's not a fantastic operator for common usage because of this.

There are valid orders of operations, such as depmas which I just made up which would make the above expression extremely ambiguous. Completely mathematically valid, order of ops is an established convention, not mathematical fact.