To stick with the inverted pendulum example. Instead of moving the base backwards to move forwards, move the top forwards to move forwards.
You can eventually turn the bike by just leaning over. But it's painfully slow compared to counter steering. California Super Bike school demonstrates[1] how sluggish body lean turning is compared to the speed and precision counter steering offers.
What's more that counter steering is also less effort. Greg Widmar (Motojitsu) demonstrates it perfectly[2] with a 1 finger counter steer demo on a 550lbs motorcycle moving at 80mph; he barely has to push the handle bar to drastically turn the motorcycle. Contrast to all the muscle and energy necessary to move your upper body around and hold it in position as seen in the Calfornia school's demo.
Subjectively, my new gravel bike is considerably less stable than my road bike, and my road bike wasn't as stable as my tri-bike. The road bike we easy to steer and I could easily ride it with my hands off of the handlebars. The less stable feeling gravel bike on the other hand feels quicker to steer, but I wouldn't try to ride is without using my hands.
Regarding your example: It's actually suprising, because Gravel bikes are supposed to be more stable than road bikes (less turns on gravel roads, and the extra stability offroad is helpful). Cyclocross bikes are the less stable cousin of gravil bikes - they are supposed to turn quicker for race courses. But since all bike categories have lots of models inside them, there's always a full spectrum in terms of geometries.
At the extreme end of bikes are downhill bikes, which have super long wheelbases and relaxed steering angles (< 64°). That helps them maintaining their course over super rough surfaces, besides an abundant amount of suspension.
[1]: https://twistedsifter.com/2016/04/artist-asks-people-to-draw...
