Don't organisations already follow this? Atleast for their workers.
People getting into a public or private job have to show that they are eligible.

Regarding meritocracy at level of society:
I think it's going to be difficult in reality.

1. Who appraises the merit of people? Who defines, maintains and updates the standards/methods used for the appraisal?
2. Is there a system for continuous quality check? It'd be needed to maintain the system as a meritocracy.
3. How is the quality check system preserved in the system?
4. Who appraises those who appraise?

In the case of an organisation, the leaders/owners of the org can choose workers with merit. But the owners themselves are not appraised, right? Unless they are in some co-operative org or so.

Perfect meritocracy seems very difficult to implement for the whole of society.

I think democracy(which gives due importance to scientific temper and obviously human life) is a decent enough system. We can iterate on it to bring up the merit in the society and its people as a whole