1. The most commonly used (physical) self defense technique of aikido is being able to take ukemi on a hard surface - particularly if you drink
It's been said before that trips, slips and falls are more dangerous than axe-wielding lunies (for most of us).
2. I too am grateful for mats for allowing us to practice certain techniques and absorb more over time. I would again however stress how they can benefit nage
by making the ground connection easier to feel - try practicing to the point of balance breaking on wood - that way you can feel the point without having to go to the doctors
You may also find that turning on a hard surface is easier on the knees.