It doesn't have to be super natural either, though. By the nature of it's existence, the universe proves that there can be chains of events spawned that completely undermine our current treatment of causality. A realistic model must include at least one of the following:

1) Events with no cause such as the beginning of the universe or broader multiverse, depending on your beliefs or 2) Infinite regressions of causal chains if you believe that the universe or God (or a god) has always existed or 3) Some combination of the above.

In all of these, somehow there can be uncaused effects, but in 1) and 3) some causal chains can just begin existing, like free will would require.

If uncausal events were so common, wouldn't they have been discovered in laboratory conditions by now? They'd be messing up experiments everywhere.

You might even say that such events would be experimentally indistinguishable from random events. Or practically identical.