We could argue that it could be whenever they can independently present their ID, pick up their ballot paper, mark it, and submit it in a ballot box (this is the procedure in the UK)

be voting as a proxy to a parent and wouldn't be able to reason well enough to represent their own self interest.

This already happens in the UK with the voting age at 18 (16 for local and devolved elections in Scotland). Provided they still have a right for an anonymous and independent vote, I don't really see much issue with this. Parents generally do have rights over their kids. While I don't believe a parent should be able to literally submit a ballot on behalf of their child without consent, it is quite standard that children follow their parent's beliefs if/until they know otherwise. The vote is still representing a living, breathing, human. A citizen/voter of or residing in said nation. It's just that they are under their parent's domain and purview until a variable age. A parent can just as easily convince a somewhat disinterested or disengaged 24 year old child to vote for a poor candidate as they can convince a disengaged 14 year old to vote for a good candidate. Or the 14 year old could be more politically engaged and informed than many 24 year olds (I believe this actually is the case) and they would want to vote for a candidate, while a disengaged 24 year old is just voting for who their parents told them to vote for.

I genuinely don't think it's a bad idea. I think the only restrictions there really should be on voting is citizenship and residency (in the UK, voting is restricted to Commonwealth, Irish, or EU citizens who settled before Brexit and are residing and registered to vote in the Kingdom at the time of the election)