Intel did have a product like that but it's been discontinued: https://en.wikipedia.org/wiki/Intel_Quark

AMD even had two of them. Their own: https://en.wikipedia.org/wiki/AMD_%C3%89lan and based on the Cyrix x586 after they acquired them: https://en.wikipedia.org/wiki/Geode_(processor)

They weren't even that bad considering the little power they needed.