What we forget is that two-wheeled vehicles drive themselves. There is a stable feedback loop built into the geometry, akin to an aircraft with a good dihedral wing. You have to force the machine to corner, then back off to allow it to do its thing. See the rider in red in the above video. He leans the bike to initiate the turn but then is actually leaning the other way once the bike is cornering/slowing due to the gyroscopic forces now pushing the bike deeper into the corner. Cornering a two-wheeled object is vastly more complex than handlebar pushes.

https://en.wikipedia.org/wiki/Countersteering https://en.wikipedia.org/wiki/Dihedral_(aeronautics)