I will say this a bike that can keep up with traffic is alot safer than a bike thats being continually taken over by bigger cars, in my eyes they are safer for everyone...
My Mum and Dad also had to put up with a son that was a bit shall we say reckless. I've ridden bikes since I was around 6ish (italjet pack 50cc was my first ever bike) and used to race a rs 125 when I was 12 til 16 (which my Mum hated) and I've fallen off quite a few times and I'm now 34.. The only time i was ever injured was on my first trials bike when I was around 10 (yamaha ty175) which only did about 40 mph, I broke my arm at a slow speed, around 5-10 mph, it was just unlucky.
But (apart from the trials bike episode) I've always worn good safety equipment, it is essential. When you own a bike chances are, even if it isn't your fault, your going to come off one day. Just be prepared for it!
A good helmet is essential...as is proper gloves and a riding jacket with armour preferrably back protection too, although back protection is more important when your top speed gets higher as when you go 'down the road' the safest way for you to be is flat on your back!
A good set of boots is also essential!!!! Many people overlook this for their kids (and themselves) and that's a really bad thing, your ankle will be the first thing to snap if you come off with the bike on top of you!
I've always worn a good pair of proper motorcycle boots (work boots are pointless) make sure you've got good protection round the back of the ankle. I even have crash bobbins on the top bolt of my rear sets, on every bike i own, it stops the bike crushing my leg when I come off.
If your kids are like I used to be at that age the only way they are going to learn is if they come off and teach themselves to slow down. So just make sure they are prepared!
But better they learn this lesson on a 50cc bike that does 60mph that weighs less than 100kg than a 1-2 ton car that's going to take out them and a few others!!