But where are they assigning you the ID from? That data has to be somewhere, and it will be able to be modified legitimately, which means you someone will find a way to modify illegitimately.
You can generate an infinite number of unique IDs. That’s how the whole block chain works.
In Bitcoin your proof of identity is your private key. Nobody can assign a private key to you. Your computer or phone or hardware wallet has to generate it and keep it secret. The private key has a corresponding public key which is hashed into an address which you advertise to everyone. If someone else tries to claim your address they cannot because they don't have the corresponding private key to sign a challenge verified by that address.
I haven't watched the youtube and probably won't but here's how I would run a voting system. I would transfer a token amount of bitcoin to your public address. In order to vote you would transact that token amount of bitcoin back to my address along with your vote. The vote would have to be a small encrypted chunk of data stored in the blockchain (there's a size limit on that, not sure what it is). Then I would tally your vote by decrypting it.
Nobody else would be able to steal your vote. Nobody would know how you voted, although the encryption of the vote is a weakness IMO because it would depend on a secure tallying system. Everybody would know whether you voted or not because that would be recorded on the blockchain in perpetuity. There are probably other problems with what I described but I think it answers your question.