Bicycles are entirely stable without a rider as long as they’re moving. The human is only really necessary to provide motive power. There are a ton of videos showing this.
It is totally unlike the intentional instability of a modern jet fighter.
That relies on the front fork being at an angle, though, doesn't it? If they made it straight down (which is the obvious choice) or pointing backwards, it would be much, much harder to ride.
Maybe in spherical cow land, but in the real world bicycles don't get very far without a human to maintain balance. It would fall over the first time it had to ride over a piece of debris on the road.
It is totally unlike the intentional instability of a modern jet fighter.