You are in some regards introducing a few questions here
I was trying to think of requirements for building an aircraft that
would be accessible to the masses
Bringing aviation to the masses is only in part related to the aircraft its self. For what its worth the Piper Cherokee 140 can be had for less than most new cars and has what has been called "Very Benigin" handling some might even say making it to safe. The plane like most GA planes glides very easily and practicing engine outs is routine to get your license. Which brings up the more important point. The current US regulations set fourth by the FAA makes it much tougher to fly a plane (although sport pilot has helped this) than it does to drive a car. To be honest it does not take that much to legally drive a car here in the US. Learning to fly an airplane is a significantly larger task, it takes an investment (anywhere from 7K-15K depending on local flight school costs) and more time than learning to drive a car. This is really what keeps the masses from flying.
For what its worth new planes are not cheap not only because they are expensive to build but because FAA type certs are not easy to come buy.
and the first thing I thought of was safe landing in the event of
Engine failure is, (assuming there is no fire involved) a recoverable situation as long as there is an open field or even a local parkway to put the craft down. Small planes (and most planes for that matter) glide fairly well and can be maneuvered under glide with ease.
or other catastrophic mechanical breakdown.
The problem with this is that most of the clean handling characteristics of small GA planes are predicated on the fact that the plane is as it should be. There are a million and one things that can break but may will cause a situation that will alter the handling or flight characteristics of a plane like asymmetric flap deployment or snapped control cables/disabled flight controls or even critical air frame failures like the 2008 incident involving a Pilatus PC-6.
could glide safely with no control input simply based on the way the
frame of the aircraft was designed
As has been mentioned most GA planes (at least the slower trainers) are made to return to a safe attitude to some extent. It should be noted that this often requires some kind of minimum altitude and many accidents happen at low altitude when the plane simply does not have time to recover. Some of this may also be effected by things like trim which if set to its limits has an effect on the planes handling.