NR, your post is much too simplistic and much too wrong!
In spite of ticket prices going to the floor, air safety has always been improved and still is inclining in relation to miles/seat offered.
Also it has to be mentioned that low cost carriers are very safe compared to higher cost business models. There is no direct connection between costs of an airline and air safety (the mentioned Alaska and UA are conventional airlines). The only safety relevant factor is culture and safety awareness in management.
Dani