Earlier quoted context omitted.
I'd go further than just remove "fundamentally" from that statement. I'd say the entire statement is false. Getting rid of meritocracy is "Everyone gets an A+". Teams will quickly get in trouble if everyone got A+ for "works well with the team" but some should've gotten a D- or an F. Meritocracies don't have to excuse bad behaviour if they simply penalise it. Perhaps those stuck in bad situations and complaining abou…
Meritocracy means that a political system is organised so that the "meritorious" get power, where merit is based on performance. You are talking about getting rid of ranking, possibly the concept of merit. It isn't possible to have a meritocracy with no concept of merit, but that is much stronger than not being a meritocracy. For example, I could rank a team of 5 from A+ to F, then put cousin Ahmed in charge because…
To use your example, your cousin was put in place due to nepotism. This is very much covered by my "some other ism" as corruption or at least bad behaviour. Cronyism and nepotism both bypass natural "best person for position based on merit" selection criteria.
Integrity is well within performance measures under a meritocratic system, eg police who are corrupt can't be seen as acting as the ideal for police officers or authority by any useful measure (merit). If you hired your cousin that nepotism impacts both yours and your cousins integrity and therefore merit. This bypasses the meritocracy and is actually simple corruption.
Plenty of other "isms" are also really just corruption in various forms: sexism, racism, tokenism, ageism. I'm sure there are plenty more.