First, it's important to note that when I talk about equality I mean statistical equality within acceptable margins. I.e., not that all people personally have equal power. As to your question, it's a matter of values. As I said in another comment, Western democratic (aspirational) values are such that all lives have equal value. Your personal values may differ. We can't justify our values based on some mathematical formula; that's the meaning of values. They are core beliefs.
Nevertheless, we could point out some obvious problems with different value systems from the Western democratic ones. For example, how is it even possible to distribute anything based on virtue and competence? We cannot distribute power based on actual competence and virtue, but only on perceived or measured competence and virtue, and that is very different. Measured competence and virtue are circumstantial, and in our real world (as opposed to some imagined utopia), reality is that power may strongly influence circumstance (and so our perception of competence and virtue). Say, if a powerful country exploits a less powerful one, steals its resources and enslaves its people, it creates a circumstance where those exploited people may have adversarial conditions to display their competence and virtue. So we would say that even if our values were such that we believed that power should be distributed based on competence and virtue, doing so would be impossible, and attempting to do so (based on measured competence and virtue) would actually result in something very different. This is why the term meritocracy is satirical (or, at least, it was coined as a satirical term), because it's obvious that true merit cannot really be measured, and any attempt at meritocracy would be no better than a system based on, say, hereditary value (nobility).
Having said that, to some acceptable degree, even in democratic societies we do want to reward virtue and competence. We put criminals in prison (taking most power from them), and reward competent virtuous people with success that imbues power. But we don't want the disparity to grow too large because we're aware that 1. our measurement of virtue and competence is flawed, and 2. too large a disparity causes great harm to freedom.