I think it's important to notice that periodicity of bitcoin is not some emergent phenomenon happening for unknown reason. It's build into the bitcoin in form of reducing the rate of supply by half roughly every 4 years.
So do you really have to be hit in the head 20 times before you notice it spins?
So your claim is that a three year cycle is driven by a four year cycle?
Besides, the bust shouldn't be driven by the mining of new coins anymore. When a huge number we're being mined as a percentage of the total btc supply you could make that case. But now, the difference between generated btc now and after the halving is negligible.
But your overall point that causality linked to external factors is correct. It's just "the mechanism is halving the rewards" hasn't happened enough times to be valid because halving isn't reliable enough yet.
So do you really have to be hit in the head 20 times before you notice it spins?