API: prohibit non-numeric dtypes in construction of IntervalIndex

[jreback]

xref #18997

prohibit construction of non-numeric sub-types for IntervalIndex, e.g. object and categorical. Not clear utility and causes a messy implementation.

[jreback]

cc @zfrenchee
cc @jschendel
@shoyer @TomAugspurger @jorisvandenbossche

[jschendel]

To be clear, do we want to disallow non-numeric dtypes just for IntervalIndex, or for Interval as well?

[jreback]

yes

[shoyer]

In theory, it makes sense to have string intervals, e.g., the first and last name on each page of a phonebook. But our current IntervalIndex indexing (with the interval tree) does not support efficient lookups for non-numbers.