Your cycling fallacy is…
“Cycling involves a risk of collision and therefore should require insurance, like motoring does”
As a mode of transport, cycling does not present substantial risk to people or property, which is what mandatory insurance is designed to mitigate.
This fallacy suggests some sort of parity between cycling and motoring, but the danger posed by driving a motor vehicle is far, far greater. This is why driving commonly requires some form of minimum third-party liability insurance – the risk of causing property damage or serious bodily harm to others in the event of a collision is so high.
Added to this are the logistics and costs of enforcing such a requirement, the question of whether children would need insurance before being allowed to cycle, and what exactly counts as a cycle – for example, many people use such vehicles as mobility aids.
The likely outcome of requiring insurance for cycling would be fewer people cycling – and as cycling is a mode of transport which can greatly benefit society in general, suppressing it by adding barriers to entry would not be a good thing.