Rafal, there is no right or wrong answer here, and as with CI and other measures, I believe the LER is something to be considered part of the exposure/development decision, not the sole determinant. Said another way, it should be somewhat flexible. Since I'm at least as interested in local contrast as total contrast, I don't target paper grades. I include expected print manipulations (burning, dodging etc) in my negative exposure/development decisions. Simply put, it depends on the scene. All these methods work fine for subject brightness conditions within a range. Outside that range, some flexibility and deviation is often helpful.
Ultimately I'm not sure the various writings/methods are really in conflict. Not only is the context important, it also depends when things were written. Keep in mind materials have changed over time. Films can record longer luminance ranges, and variable contrast papers were not really taken seriously until well into the 1980s or even 1990s. The limitations have changed.