Mesa is an opportunity like anywhere else. Get your time and experience, and move on. No one gets "stuck." People decide to stay or pass up other opportunities thinking they will be better off. You are only going to settle for the "big five?" That's your decision, just remember that it used to be the "big eight" or what ever, and they had flight engineer positions to fill as well.
Fewer airlines to move into, with fewer positions available. In the past people had far more choices and thus more chance of moving into mainline.
Self reflection and a willingness to try something completely different to escape the regionals is well advised for those who want out of it.