For example, gyroscopic-forces-as-stabiliser don't need the Schwab paper's "ton of math" to be undermined. A simple counter-rotating wheel was used empirically at Cambridge to show as much, alongside notes that gyroscopic forces are relevant to the dynamics of a loaded bicycle, but misconstrued; far from assisting to hold it upright whilst ridden, they induce instability at the beginning of a change in direction, and more so at speed, a phenomenon (counter-steering) familiar to cyclists and relied upon by motorcyclists.
Then there's a simpler observation that can be made: people have to learn to ride a bicycle. The fact it stays upright when rolling unloaded, but not when loaded, is indicative of how small the gyroscopic effect is, not how significant it is. Ergo, that argument would suggest, it is tiny shifts body position that contribute all of the stability.
And then others, proposing further explanations, etc etc ad nauseum.
I have come around to the view that in fact they don't stay upright, and they are almost always falling over, but in a many-branched configuration of the universe our observer effect sends us preferentially down the vanishingly unlikely path where they didn't, and there are an uncountably many alternatives of Me that have nothing but knee scars to show for it.