> you can just let go of the controls and most aircraft will be stable

This is not rule.

Some planes named "friendly to novice pilot", and are stable, others are not, and this is somewhere predictable when design.

I even hear, Lindsberg, when was preparing for his flight, asked designer to make his plane unstable, because typical stable flight is very boring and he scared to fall asleep.

In other cases, modern planes like 737s and larger scale, usually considered to have zero stabilization in design and if need, stabilization created by electronics (navigation system is usually made as very high precision inertial platform, so could in most cases know, how should fly to looking stable). This is because design stabilization costs additional resistance, less payload and more fuel consumption - for 737 scale it is about 1-3 additional passengers and few percents of range. Military planes and some aerobatics now are designed unstable for better maneuverability.

I don't say, this new trends are good, just notice.

Just about all useful airplanes are stable in pitch (either statically stable aerodynamically, or closed-loop stable with an enhanced stability system), but roll stable aircraft are relatively rare. Most aircraft are slightly spiral unstable, at least beyond a critical bank angle; but the double time constant is so slow that it's a non-issue.