If a village Kage chose to go with that sort of test, similar to Hidden Mist, that would be on them. At the end of the day, the talk of which rank can be ANBU and what is required etc is pointless because every village will be different based on their leaders.
[Rant ahead, if you're lazy, stop here]
Now, keep in mind that Kage are going to be players and therefore can run their village however they want (After all, that is what a Kage does) and therefore can choose someone to be in charge of picking ANBU like a right-hand man or through a test or maybe even just Jounin ranked alone. This is all down to the individual and not to be judged on a system.
How I would do it, if I was to be a Kage, would be to check the current ninja of the village's progress with missions, success rates and how they do with others. I would pick them based on overall skill and not their ninja rank and I would most definitely not make them fight, though it sounds appealing. In fact, if I WAS to be THAT guy, I would host it in a quiet place in Perma-death and last 5-10 standing will become ANBU whilst the rest perish. XD
Anyway, that is pretty much it. Every village different due to players being Kages which run their specific village the way they want to.
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