That kind of stable flight is ok for an unmanned vehicle, but I don't think a passenger/pilot would be delighted abut that kind of accelerations and spin.
The Cirrus SR22 single engine aircraft has this (their system's called CAPS.) It lets you sail to the ground in the event of some catastrophic failure preventing you from landing the aircraft safely. http://en.wikipedia.org/wiki/Cirrus_SR22
I suspect the parachute would be far too heavy. Also, jets fly very fast, and the jerk when the chute opens would likely rip things apart.