Your “simpler is better” is hard to apply. One way of thinking about models where there are no intermediate cardinals isn’t that S doesn’t exist. But that T, a mapping from S to either the naturals or the reals, does exist.
And T will also be something you can’t explicitly construct.
Also, the axiom of choice basically says “there exists loads of sets that can’t be explicitly constructed”.
Your “simpler is better” is hard to apply. One way of thinking about models where there are no intermediate cardinals isn’t that S doesn’t exist. But that T, a mapping from S to either the naturals or the reals, does exist.
And T will also be something you can’t explicitly construct.
Also, the axiom of choice basically says “there exists loads of sets that can’t be explicitly constructed”.