Yes in that perfect world first off no one would ever crash and most important everyone would be sucessful in the sport!
But in hindsight, If that were the case the never ending supply of wonderful projects recovered from the trash cans of every field would dry up and the supply of bargain equipment would be no more. Not to sound unkind but perhaps a perfect world is not so perfect.
So not to stray to far, Yes Texy most trainers attempt to reach a degree of positive pitch and lateral stability (sometimes called self-righting ability) and that is the idea for trainers and some other types as most of the posters mentioned. As your skills progress you will probably find airplanes with more neutral stability in all three axis' more enjoyable.
At any rate Texy welcome to the sport and hang in there you will ultimately find this endever very, very gratifying.
John