Why does std::span lack size_type?

The original proposal P1022R0, back when it was called array_view, had a size_type member. It was removed in the first revision P1022R1 as part of the simplification, as it wasn't needed because size() and element access were, at that time, using the signed index_type (aka ptrdiff_t). At the Kona 2019 meeting, that decision was changed in P1227R2 by changing index_type to be size_t.