I did suggest changing it for motor vehicles as well ; it would be administratively simpler to identify the rider/driver than the machine ; you are assigned a number at age 11 , when going to high school , and it stays with you for life , regardless of driving tests taken or not , particularly if you were not restricted as to how many vehicles / cycles you could have as an individual driver/rider . For cars/vans etc , it is just a matter of the driver having his own plates which he/she slots into the holder before taking the wheel 9 could even be thin foldable plates which can be easily carried and slotted into a holder with perspex cover .There are two further problems, one practical, the other more fundamental.
Put the number on the vest. Now try reading it as it flaps, in the breeze, gets obscured by a rucksack, etc, etc. Drape it over the rucksack? How big is this vest? Then watch it doesn't get caught in the spokes.
Nowhere do we have to wear anything that identifies us in public. Not even cars. The registration mark on a car identifies only the car - not its driver. The driver still has a legal right to deny driving it (though there is a sanction for this). You may or may not agree with the correctness of that situation but it would be fundamentally unfair to deny a cyclist the same right for doing the same thing ie, using a wheeled vehicle on a public road. To change one, so must the other be changed and I doubt there's much appetite among motorists for that - or any great need.