I commute on a road bike with 23mm 120 psi tires and the only place I feel any hint of instability is one stretch of newer, larger gravel. It feels as though I am skating across the surface a bit on that patch. I do regularly ride much older, much more packed down gravel trails and while a road bike isn't the perfect bike for this, it doesn't feel unstable.

Wet wood bridges on the other hand...