You can imagine waterfall of sand - the fluidity here comes from all those small sand particles moving simultaneously.
>>>Physics steeped enough in quantum theory do understand QM enough to have meaningful discussions free (at times) of rigorous math.
That sounds a lot like gate keeping and has no actual backing - to understand QM you still need to understand Physics, as mechanics of both of them are explaining each other - the scale is the only difference.
The idea is that you can discuss using hand waving while drinking coffee, but after that you must write the complete mathematical calculation, so there is no gate keeping.
Most of the times the formal version with equations agree with the hand waving, but sometimes you have nasty surprises and must learn to hand wave better.