"So do we now rely on software to make things fly that shouldn't?

I guess you could say that this can be the case, particularly with fighter planes.

See https://en.wikipedia.org/wiki/Relaxed_stability, especially the Intentional instability bit:

The latest generation of fighter aircraft often employ design elements which reduce stability to increase maneuverability. Greater stability leads to lesser control surface authority, therefore a less stable design will have a faster response to control inputs. This is highly sought after in fighter aircraft design.
A less stable aircraft requires smaller control deflections to initiate maneuvering; consequently drag and control surface imposed stresses will be reduced and aircraft responsiveness will be enhanced. Since these characteristics will typically make control by the pilot difficult or impossible, an artificial stability will typically be imposed using computers, servos, and sensors as parts of a fly by wire control system.