Obviously 13 is too young, but remember Jerry Lee Lewis married his 13 year old cousin, quite legally, in the 1960s, I believe. There was a bit of an outcry in Britain when the press found out.
In the later 1800s age of consent in Queensland was 12, in England 13 and in Russia 10. Imagine - 10!!! Of course, then as now, kids mature at vastly different rates.
Adults are supposed to protect kids against themselves, which is another reason older adults should never have sex with under 16 year olds.
When I was a very inexperienced 17 year old, I started going out with a 27 year old architect. I though he was lovely, but I was terribly innocent and immature, and when he realised this he dropped me like a hot brick. I was heartbroken, but I realise now he would have felt like a paedophile if we'd had sex. Some men actually do the right thing!
(2 years later my immaturity paid dividends - I went to live in Austria to improve my German, and ended up being totally fluent and without accent - this can usually only happen before the end of puberty)