It all depends on why. If it's just to enjoy a ride, then maybe not - I'm 17 now and have been driving a car for 5 months but just after turning 16 I took my CBT and got a moped.
For getting to college and my local football games it was awesome! I wasn't fond of the 30mph speed cap as I did think it made it more dangerous, but nonetheless having the bike made it easier to commute and all around made things cheaper for me. It cost me around £2000 total which covered: CBT, brand new moped, jacket, boots, gloves, helmet, tax & insurance. There are probably some other things in there too, to be honest.
Petrol was dirt cheap, which is definitely what made it worth it. I'd use it for the likes of nipping to the supermarket, going to/from college, sports games, etc. and I didn't regret getting it.
Although, as aforementioned, they're dangerous. Especially 50cc bikes. Cars would overtake me without care, pull out on me, pedestrians would often walk out in front as well. Driving on fast roads was somewhat intimidating when trying to stick to the side and let cars overtake, but I managed to avoid them when I needed to.
I'll be honest and for probably a month or two before I turned 17, I took my dads 125cc out a lot since he wasn't home, and this felt much better to ride in terms of road safety and keeping up with the flow of traffic, but still had its risks, of course.
So to finalise, if its for fun, don't bother, if you'll actually use it for commuting a lot, then go for it.
** awkward moment when I realise this is a year old.... someone may find this useful I guess! lol