There is nothing wrong with plural voting, other than the fact that all historical occurrences of it on a national elections scale were designed to favour certain groups on questionable bases (white male property owners, for example). The concept of "one person, one vote" is a reaction to the unbalances of plural voting, and it's both a simpler and a fairer approach. The crucial difference between the two systems is that it is a lot easier for a society to judge whether a voter has been harmful to the society than to ascertain whether a voter is more valuable than average.
Let's assume a simple election model, where citizens:
- Get one vote at age 18, and
- Are excluded from voting if incarcerated.
The age requirement is an arbitrary limit, that has been challenged since at least the early 20th century. Demeny voting, if established, would be a very interesting mixture of the two systems, as at one hand minors would get a vote, furthering the "one person, one vote" concept, while at the same time their parents would get more than one vote. In any case, I'll ignore it as it was present, in one form or another, in all examples of plural voting, and it's not really a trait that separates the two systems.
This leaves us with only one requirement for political franchise, a requirement that is very close to being objective, assuming of course we trust our model society's justice system. And if we don't, I think it's fair to say that the whole discussion is moot, we have bigger problems than our voting system. Similarly to a trusted justice system, other requirements that are commonly present in "one person, one vote" systems are based around trusted institutions, for example excluding mentally unstable citizens from voting would require that the population generally and overwhelmingly trust the society's health system.
Now, imagine that our model society is trying to move on to plural voting, who'd get a second (or third or fourth) vote? If you manage to define "doing more than average for society" in a way that will be as clear as a trusted justice system and will not have certain groups of people calling for your head (on a platter), congratulations, we've successfully moved on to plural voting. Expect a riot in 6-8 weeks.
Everyone having the same weight is a naive goal, "one person, one vote" is more a system of minimizing the potential for abuse than one of idealistic equality. I don't think plural voting would be considered a less democratic system, if we were able to come up with a balanced (or at least apparently balanced) and (mostly) frictionless way of determining who gets the extra votes, similarly to how forms of weighted voting are not generally considered undemocratic and are practised and widely accepted in several democratic countries and institutions. It's not an inherently wrong system, it's just unrealistic to believe that a society will overwhelmingly accept any method of measuring one's contributions to it.