My biggest issue with this would be how this affects children. Learning to cycle is such a useful skill and many older children rely on their bikes to get to and from school. Would you have them wait until they are 17, like car drivers?
I would rather campaign to change the system.
British roads are not built for cyclists. Look at continental Europe, where cycling in general is far more common, but cyclists have their own path alongside roads, so they don't continuously risk their lives due to impatient drivers.
It also gets them out of the way and makes waiting at a traffic light far less dangerous (which contributes to the number of cyclists who change to pedestrian paths at traffic lights).
Cycle paths here are strange - I have seen them change lane from the pedestrian to the cycle side all of a sudden through bad road marking, I have seen them suddenly end after a few meters and most of the time they simply don't exist.
Where I am from, all children learn basic traffic rules in primary school - who has right of way, what traffic signs mean etc. and then take an exam similar to the car theory and practical test where they gain a "cycle licence". It's not a legal document and they'll never be asked to present it, but it does make them far safer on the roads. So why not throw out something less useful from the primary curriculum and look at road and cycle safety instead? It would help so many down the line with driving, too.
I would, however, make helmets and visible clothing mandatory, as well as what bikes themselves have as standard. Bikes sold over here are extrenely poor quality compared with continental Europe; they are almost just frames and everthing that should be standard - lights (why are they battery operated and not dynamo operated?), a stand, splash guards appear to be optional extras. And why do British bikes only have a hand brake, which is far more unreliable and dangerous to use than a back tread brake?
Compulsory licences are not the way forward, but much can be done to improve conditions for cyclists and make them safer to start with.