So we do know how the bikes that actually are 'bikes' work at least to a very large degree (engineering vs math), but we don't know all the possible physics which can enable an arbitrary two wheeled construct to be selfstablize when perturbed while in forward motion.
I completely understand the point your making. However, at when making a technical argument and then generalizing the end results, we can end up in a situation where the truth of the technical argument no longer strictly implies the truth of the generalized/summarized result. I feel the statement 'we do not know how bikes work' has crossed that line.
I suppose it depends on how you look at it, or perhaps on whether you're interested in how a bike works versus why a bike works. How is relatively easily answered; as the bike tilts it steers into the tilt, moving its base back under its center of gravity, in a way which damps itself thus getting back to upright without oscillating repeatedly or falling over.
Why it works is the open question. We know that it's some combination of gyroscopic effects, rake, trail, and the different centers of gravity of the frame and fork, but we don't know the precise relationship between them that allows it to work.
I completely understand the point your making. However, at when making a technical argument and then generalizing the end results, we can end up in a situation where the truth of the technical argument no longer strictly implies the truth of the generalized/summarized result. I feel the statement 'we do not know how bikes work' has crossed that line.