Children pay taxes if they earn money, as far as I am aware, such as is the case with child actors and so on.
It was you who first wrote:
on the basis that children (in this case 6 year olds) aren't legally responsible for what they say or do
The age is 10 in England according to government website.
https://www.gov.uk/age-of-criminal-responsibility
Why should minors not be allowed to vote? My best reasons are that 1) generally they are not interested voting 2) if they did vote they would just do what others suggest and 3) they don’t understand many of the issues.
On the other hand you could say much the same about many adults. So are they good enough reasons? Or are there better reasons? I don’t know but I think it’s an interesting idea, without needing to call anyone regard.