Makes no sense other than we had just fought a war over the concept of states' rights overriding federal protections. Hypothetically, they could have narrowly-tailored the 13th through 15th amendments to end slavery and do little else, I think it is possible that lawmakers of the day came to a rational conclusion that the next time the states challenged federal authority so brazenly, it wouldn't be over slavery but over some other issue of fundamental rights... And if the protections laid out in the Constitution were good enough for people when exposed to law at the federal level, they should be good enough for citizens of the states as well. One certainly can't expect that anyone would have benefited if, hypothetically, Georgia were to dedicate itself to Roman Catholicism and declare all federal laws null and void, replaced by the law from the Vatican (a scenario that could have been possible prior to the 14th).

One advantage the chosen approach has is, in a sense, interpretive simplicity, even though in practice it strips much authority from the states and moves it up to the federal level.