I can only imagine in my head parents took their kids into the voting booths. Since this amendment has only been around since 1971, I would assume people would know by then how it could be abused. Is it just an amendment to unify the voting system vs old state laws which would prohibit children from voting?
Basically, yes it was to unify the voting system. The law was you had to be 21 to vote in federal elections. Some states allowed 18-20 year olds to vote in state elections.
There was a big push to lower the voting age to 18 since 18 year olds were being drafted to fight in Vietnam.