It isn’t a good saying, in the sense that what the speaker means by “good times,” “bad times,” “strong men,” and “weak men,” is so open to interpretation as to be meaningless. I like your interpretation. But I think the expression is often interpreted with “strong” implying a certain sort of roughness/propensity toward violence.

Anyway, it is clearly not accurate—“good times” and “bad times” must at least be opposite, however we define them, right? But we see all sorts of countries in history that have multi-generational reinforcing stretches of excellency. And we see many countries that suffered from many-generation-long stretches of bad times. These good and bad men don’t seem to pop up anywhere near as reliably as the expression claims.