Thank you for your insight. Please forgive me for the tongue in cheek responses on a few select thoughts.
system in which the most capable person isn’t in charge?
Every system since time immemorial. And which will continue until "most capable" is better defined, objectively determinable, and implemented by the greatest power.
popularity contests
The foundation of every democratic, republic, and individual choice based system today.
it’s very difficult to determine merit
Very true. Considering all people under any one governing system would never agree on what is virtuous, worthy, valuable, honorable, or respectable. Just try to convince people who believe, "If you aren't cheating, you aren't trying," to believe otherwise. Many Chinese believe if you didn't cheat to succeed, it's your fault for failing. Consider it a pitfall of cultural reconciliation.
a group of peers would vote for someone within the group
Each one is worthy within the scope of their domain of expertise, in which they have demonstrated merit.
How are resources distributed between groups? Equally? Every time a new group arrives a new slice of equal pie is collected piecemeal from the other groups and handed over? Do we compare apples and oranges to determine who gets more resources. Who sits in the "administration" group to judge merit between two disagreeing groups?
How long does a merit last?
For as long as you can demonstrate it. If someone better comes along, they should take your place.
What's a retirement plan look like? Or is this still an ownership system where you can hold on to any property indefinitely and determine it's ownership upon death?
Brilliant mathematicians get rewarded with what?
More mathematical problems. And ideally, also lots of money and babes.
A good workhorse is rewarded with more work. A never truer statement. Merit sounds exhausting today.
it’s a cultural problem. Meritocracy can only work if there’s a critical mass of people who believe in it, understand it, and enforce it socially. The same can be said of democracy, capitalism, and basically any other social order.
I'm 60% with you. Regardless of how detrimental a government is, culture controls most of how we think and feel, just look at government trust ratings by country. However, there's still more to be accounted for. Implementation and population still count for something. Keeping culture unchanged is futile, everyone comes up with their own ideals and injects them into the next generation, thinking it'll make things better. Not to mention corporate ideals, such as the diamond's are forever from jewelers, personal responsibility from tobacco, apple is a status symbol from Apple, and on and so forth.
Back to topic: Most people don't and won't care about the government, they just want the government to solve their problems or get out of their way. Getting a population to "believe in [government], understand it, and enforce it socially" is a much taller order than it sounds. For verification: the Americans, with the two most rubbish candidates you could possibly find, all seem to think voting for anyone other than rubbish R or rubbish D is throwing their vote away. Let alone the significant remaining percentage who think their vote doesn't count for anything at all.
Checks and balances entail compromises and disagreements, which individually prestigious people should be subject to. As you said, "no one should be above the law." If the meritocracy is not the law, who is the law?
Thank you for taking the time to read and think.