I've addressed this a few times, but I will do it again.
5/3/1 does not make you progress slower than any other program. The last set has you shoot for a PR. This means it's up to YOU to make the progress, not the program.
For example, let's say, for your 5s week, you're supposed to bench 135lbs. You bench it for 8 reps.
Next week, on your 3s week, you're supposed to bench 150lbs. You bench it for 10 reps.
Wouldn't that be even FASTER progress than only increasing the weight 5lbs a session?
Yes, the training max only increases every month, but it has no bearing on how strong YOU are getting. It's simply a number used for the sake of programming.
In all honesty, were I Jim, I would take offense to the notion you presented that he intentionally would give you less than perfect information for the sake of promoting his own program over what would be best suited for you. It is FAR more likely that Jim has developed a program that he feels is best suited for your unique situation based upon both his years of being strong along with his decades spent training others to be strong.
In the end, none of this matters. If you did Starting Strength for the first year of your lifting life and then 5/3/1 vs starting at 5/3/1, the difference would be incredibly minimal 10 years down the road. Do what you want to do,