I just recognized that generic (i.e. class-less) set charms seemingly completely stopped dropping for me quite a while ago. I just have 7 overall at the moment, one full set and one or two charms of each of the other sets. Class-based set charms drop regularly though, so much that I come across ~10 of them each day
Do the generic ones maybe only drop at certain difficulty levels, e.g. T1 or T2? I’m aware that set charms should drop more often from T3 onwards, but does this maybe stop the generic ones from dropping at all? 
those should be early sets to use during leveling to 70 but i’ve never seen them drop fast enough for me to benefit from any of them. if RNG is the culprit, sure ok fine but their drop rates should be better.
I’ve barely seen a full set of those. They must only drop up to a certain character or torment level.
It’s been ages since I’ve seen one drop.
From my own experience I could infer they only drop pre torment. And yes, as said they drop often too late for you to benefit from it. I got one at lvl 36, another at 59, then nothing till 70.
As for “proof” of what I said first, I leveled a necro alt from 1-70 by opening 6 T12 caches. Then I gave him a lot of my useless and junk barb class set charm drop. Of course they were not usable by necro, so I cubed them using 3 to 1 reroll. I was in penitent. Always got those practiced technique or slaughter charm as outcome. Then I unlocked T1 and did the same. Then only got necro specific charms while rerolling barb charm to necro
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I was able to replicate your findings to some degree with a new character, as a generic set charm dropped at about level 40
If this is the way to go, the effort of getting complete sets of those, even if just for the sake of completeness, would probably outweigh the sets’ actual usefulness…
i just started a new warlock and was able to use one of the intro charm sets. for about an hour. lol