I think everyone hits a point where the low hanging fruit of beginner's gains is all picked and progress slows down.
By beginner's gains, I mean gains that come from nervous system efficiency and form efficiency, and mobility and stability gains (from practicing the main exercises themselves as well as from any additional movement skill work that might be done along with the main training program).
These gains can come quickly and you can keep making gains in these areas for quite a while, depending on training history ("beginner" doesn't have to refer to being a beginner to strength training), motor learning ability, injuries/restrictions, etc.
But eventually there comes a point of diminishing returns. For a lot of people, but certainly not all, it seems to be moving up to 32kg, which makes the simple goals of S&S very appropriate.
At a certain weight, a "threat response" kicks in where you are beyond your comfort zone. Moving through and beyond this point takes consistent effort, attention to detail in refining technique, and intelligent progression, which can be as much about disinhibition and feeling comfortable with the load as much as getting stronger (or, on second thought, maybe that IS getting stronger).
IMO, when you hit this point, patience becomes very important, as it's easy to hit a plateau and/or get injured if you push too hard. I use the analogy of trying to break through a wall. If you keep charging at the wall trying to bust through it, you're probably just going to hurt yourself. If you can keep the wall moving backward, you can move past where it was without ever hitting it.
In a way, moving up a bell ought to get EASIER as the bells get heavier, since a 4 or 8kg jump is a smaller percentage of the total weight. This may be true for some people to a certain point, but most people will experience a clear sticking point where progress becomes harder.
