No, it wasn't limited. Everyone had the right to vote until they failed to pass a test. That's unlimited. Limited would be no one has the right to vote UNTIL they pass a test.
As a man with near perfect SAT scores I'd like to remind you that tests are bullshit. I mean I'm a huge slacker, lazy, unproductive, mentally ill, in a perfect society people like myself would not be allowed to breed, let alone vote. And yet this system advantages people like myself over hardworking citizens. Tell me, how high does your score have to be? Do you have one in mind? Have you, incidentally, ever taken this test? Would I be correct in assuming that any hypothetical restrictions wouldn't include your score?
No, it wasn't limited. Everyone had the right to vote until they failed to pass a test.
So can I just opt out of the test than? No? Than what is the point? And if the test isn't optional, than why play wordgames? You take a test: if you pass, you can vote; if you don't pass, you can't vote. Am I wrong?
So if a method to becoming enfranchised is available and achievable for EVERYONE, even the very poorest and worst off, you'd still be against the idea?
The fact is that in order to enact this rule would require disenfranchising potentially large percentages of the population. The basic principle of the modern democracy is that the only right a government has to represent its citizens derives exclusively from their consent, represented through enfranchisement. Any groups who cannot vote are excluded from this rule.
If there exist a group who must pay taxes, serve in the armed forces, be subject to laws and criminality like every other person in the country, but has no legal representation in their government, this person now exists outside the political system. Tell me, having disenfranchised these people, what if they should find themselves disagreeing with the current position of government? With no legal political means to express themselves, would it not stand to reason that some of them would oppose the government very strongly? Is it wise to build up a core of people who hate the government, are not wedded meaningfully to democracy and who believe (quite accurately) that the system does not represent them? Imagine these people grew angry for some reason or another; how might they express this anger? Can you perceive no dangers here?
More broadly speaking, from the perspective of the US this can be safely rejected, given the founding principle "No Taxation without Representation".