Imagine, for example, an engineer decided to reorder members in a struct to make it pack better. Now the semantics of default <=> have changed!
Also, as a minor nit, the optional number sample has a possible bug. I would assume that two null optionals would compare equivalently. Or is that part of how <=> should work? Should NaN <=> NaN == partial_ordering::unordered?
Note that floating point is already weird, because most languages make == reflect the ordered equals, not the unordered equals, and so the primitive equality for floats violates the reflexive principle (i.e., x == x returns false).
Otherwise you may have the strange behavior that two erroneous values are equal, e.g., 0*inf == tan(inf).
For what it's worth the mathematical definition of partial orders suggests having NaN equivalent to NaN. You're not really forced to but giving up reflexivity doesn't seem worth it (unless you want to view each NaN a it's own object).
Interestingly mathematics only defines <= for a specific kind of object. Although on it's own this doesn't give you much information about what kind of relation it is.