Whoa whoa, what you said is "the constitution clearly gives the federal government the ability to conduct federal elections, not states." This is blatantly false. I presume you discovered that when you looked it up and now you're switching gears.
Now you're mounting a totally different argument which is that Congress has the power to enforce Section 3. This is true, but that does not strip states of power to run their own elections how they see fit. This merely grants power to Congress to enforce Section 3.
You just misunderstand how the Constitution works.
Here's proof: The Constitution does not give states the power to pass laws. It does give Congress the power to pass laws. It giving Congress the power to pass laws obviously does not strip states of their power to pass their own laws.