There's a number of issues with having a young politician run for PM.
Firstly, younger people tend to change their political opinions quite quickly - mine have changed massively since I was younger. When I was about 9 or 10 I invented communism and thought it was a wonderful idea (oblivious to the fact that others with a similar level of real world experience had invented it long before me). When I was 17 I thought we lived in a police state where the police were used to stop us properly enjoying ourselves (by that I meant gathering together and taking drugs/listening to music) because if we were allowed to do what we wanted, "the man's" society would crumble. Then I grew up, studied some Economics and realised that the whilst free markets are not the perfect solution, the more we tend towards them, the better society is (to a limit). Now that I've got a kid of my own, my politics lean a little more towards "fudge you, this is mine, keep your grubby fudgeing mitts off of it".
Then there's the trust issue. Not only does this young person need to be trusted by the electorate - a fairly heavy requirement in itself. They also need to be a heavyweight in political negotiations abroad, with business, unions, etc. If they're too young nobody will take them seriously.