Simple.....
Not one to bicker, really!, but it seems the 19th amendment says it is a right. Of course the government can limit, or restrict, rights (felon voting, etc.).
If I remember correctly (not that I was there or anything), when the constitution was first ratified, only property owners could vote. Lots of people were left out of the loop at the time. Am I remembering my history correctly?
Voting is an individual power. It can neither be delegated to, nor controlled by government. You can cast a ballot on election day or you can vote with your feet and move your body somewhere more to your liking. Conversely, if you're permitted no say or movement by law, you can vote by protesting your case and hope for relief or you can vote by taking up arms and attempting to overthrow your opressor(s).
Your vote = Your power = Your ability to exercise force
And yes, the power of the vote was originally only exercised by landowners. In the early 19th century, it was widely understood that voting was force and generally agreed upon that it should be limited as much as possible. Therefore, it was restricted to those with the largest stake in government - landowners. It should also be said that in some places this included women - long before Suzy B. did her thing - and in at least four different states, free black men who owned land were permitted the power. This wasn't good enough later on down the road so steps were taken in protest (and some violence) that extended the franchise to all those over the age of eighteen.
Now even if you're too stupid to tie your shoes, you're allowed to exercise force over others so long as you've been alive eighteen years - sweet, right?