In what sense does set theory really 'provide' a foundation of mathematics when it's a later historical development over geometry, arithmetic, analysis, etc. ?

Why does mathematics which was applied effectively prior to concerns about 'foundations' need to be 'grounded' outside the human faculty for rationality and abstraction? Sets are more 'primitive' mathematical objects than groups, fields, algebras etc., but the historical development shows that if anything the more basic problems of algebra and geometry which occupied people throughout the majority of the common era are the true foundation of mathematics, rather than set theory which represents a higher level of abstraction than was achieved previously---but does greater generality really count as a 'foundation' when the causality of its historical development is reversed, especially when the construction of basic objects i.e the natural numbers is so clumsy?