Because the Military is predominantly temporary and people that march off to war and the potential to be maimed and killed deserve the vote.
That and most military votes conservative would be the side benefit.
Rather than try to impose identical qualifications across thirteen very different states in our constitution, he saw no reason not to allow universal white male suffrage, because a senate of the states would stymie the expected wild democratic ideas to emerge from the House of Representatives.
We still have a wild House of Reps, but because of the 17th, the senate has unfortunately joined in the democratic buggering of our republic.