Brian Alsruhe is a good guy to listen to. There is nothing to worry about with regards to " not dealing with heavy weights", the idea of linear progression is that you slowly ease into working with heavier weights. Most of the old school lifters trained that way (think Ed Coan).
The only problem that I see is the order of the exercises, it looks like it is more focused on deadlifts than squats. It's much easier to deadlift heavy the day after squatting than the other way aroud. If you aren't going to compete in powerlifting then it isn't a problem, but remember that Alsruhe competes in strongman. For powerlifting, you would be better off doing squat and paused bench on the first day and deadlift on the second day.
5/3/1 is OK but the basic template is low frequency per lift/body part, most people would be better off with something like this. If you are set on 5/3/1 then do something that has you squatting and benching at least twice a week.