All of these arguments try to argue that implementing meritocracy perfectly is impossible.

But ask yourself, what is the alternative? A system in which the most capable person isn’t in charge? Should we go back to bloodlines, or popularity contests, or maybe use a lottery?

I agree it’s very difficult to determine merit, and even more difficult to stop power struggles from messing with the evaluation, or with the implementation. But I would still prefer a system that at least tries to be meritocratic and comes up short, to a system that has given up entirely on the concept.

I’ll try to answer some of your questions, as best as I understand it:

Who determines merit, ability, and position?

Ideally, a group of peers would vote for someone within the group, who is the most capable, with outside supervision to prevent abuses.

Popularity contests in determining merit

Popularity shouldn’t factor into it. Only ability. (and there’s no doubt Depp is the better actor :P )

Are Athletes or Artists more worthy

Each one is worthy within the scope of their domain of expertise, in which they have demonstrated merit.

Power corrupts

Always true in every system. That’s why we need checks and balances.

Save the entire planet, then start kicking cats. Still a hero?

If kicking cats is wrong, it should be against the law, and no one should be above the law. All other things being equal, whoever has the most capacity to save the planet should be the one to do it.

How long does a merit last?

For as long as you can demonstrate it. If someone better comes along, they should take your place.

Brilliant mathematicians get rewarded with what?

More mathematical problems. And ideally, also lots of money and babes.

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At the end of the day, 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.