As odd as it sounds, the Founders of the Republic did not define who could vote in elections of federal office-holders, but left that decision to the states. The reason, of course, was to preserve the autonomy of states to protect their systems of slavery and disenfranchisement. The entire responsibility of running and managing elections for the Federal offices was left to the individual states. Which is odd, when you think about it....
Article II, Section 2
1The House of Representatives shall be composed of Members chosen every second Year by the People of the several States, and the Electors in each State shall have the Qualifications requisite for Electors of the most numerous Branch of the State Legislature.
Stevens, John Paul (2014-04-22). Six Amendments: How and Why We Should Change the Constitution (p. 135). Little, Brown and Company. Kindle Edition.
The result is what we see today. Not only do voter registration systems vary from state to state, but the administration of elections varies
Why shouldn't elections in the United States have uniform rules, procedures and systems? Why shouldn't there be national universal registration at age 18? Why shouldn't there be one standard method of identity verification used in all states? Why shouldn't the administration of elections be funded by the federal government, according to universal standards for equitable voter/machine ratios, wait-times, and voting hours?
Why should we put up with the shenanigans we see in which state officials manipulate the administration of elections for partisan purposes? Voter ID! Long lines! Arbitrary voter disqualification schemes! Restricted early voting! Inequitable distribution of machines ! Obsolete and sub-standard and insecure voting machines !
Why cannot we have uniform, standard, equitable, and well-run elections?
We cannot because of the heritage of slavery. Remnants of compromises made with slave-holders centuries ago still limit our democracy.
We need a constitutional amendment through which the federal government takes control of federal elections and guarantees the voting rights of all, concretely and practically.