What you're describing is an equal opportunity society. That's a worthy goal, but trying to redefine "meritocracy" to also mean that results in confusion at best.

Without a common language communication becomes impossible.

The normal definition of the word is that those who are best at a task should perform it. The most competent applicant should be hired for a job. If a billionaire's kid happen to be best, because of all the private tutoring they got, that's not really relevant for a meritocratic decision.