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You missed one of the points ...

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"Untouchable" castes are lowest in the hierarchy and can hope to move up in next birth by sufficiently "brahminising" themselves by not eating beef/flesh and having clean habits.>>> over several generations castes adopt habits and move up the chain by announcing one fine day they are Brahmins changing their surnames even. this process is called "Sanskritization" as described a sociologist called MN Srinivas. This happened primarily in south of India where it was possible for SOME racially impure to become Brahmins after a while. Govindacharya - if you will notice - had a very controversial career in RSS with the purist Brahmin lobby after his blood - including alleging an affair with lower caste leader of BJP. His career has got nowhere.

Again if you look at caste hierarchy - the darkest are the untouchables and getting lighter as you look up the hierarchy. Brahmins are more or less an exclusive club. Exceptions are there and I have explained the reasons.

please do some reading on caste system and caste mobility over centuries.