Any type that's super effective against less than two different types is trivially incapable of meeting this requirement, which snags Normal (0) and Dragon (1). Otherwise, the only way a type can meet this requirement is if, for all the types it's super effective against, none of them are capable of permuting into a combo that's actually used on at least one Pokemon. And as it turns out...
...so no, clearly none of those are in a position where the only type combos they would be able to hit for double weaknesses are all completely unused.
Even Normal and Dragon can hit a double weakness, but only if you happen to be playing an Inverse battle: then you could simply use Aron or Mawile respectively.