It hasn't been around long enough to "routinely" do anything on a three-year period. There have been 4 such periods. That's not enough samples to say anything is routine.
Edit: That's cycles. So I'm saying it's 2055+ before any case can be made and it's 2070+ before a strong case can be made.
So do you really have to be hit in the head 20 times before you notice it spins?
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.
The cycle is 4 year, peak to peak.
Busts are not causing by mining more. Busts are caused by greed burning out. Greed that was caused by appreciacion due to more limited supply.
Reducing supply by half is never negligible because supply balances the demand so halving it leaves half of the demand unfulfilled.
Also half of the bitcoins are worth more than double that from before the halving.