Yeah it depends on the bike big time I guess. Like you said the bike will naturally keep from going too crazy. Thats why I mentioned riding MX bikes, they dart all over the place all day long. Once you get comfey with it going where it wants to, you loosen up your riding style a ton, and build muscle memory for different senerios.
Look into the “Z” riding style for bikes. it talks about using your bodies core strengths to controll the movements of the bike. It seems a bit goofy when you first learn it, but once it becomes second nature, you will see your lap times drop, and your stamina increase a ton. Its very interesting.