I think the term generic is a bit harsh. They are alternative trading cards to the game.
Especially Carddass cards which as you know are produced by Bandai whose trademarked branding is distinct. Their trading cards were also released before the TCG. Bandai (under the Carddass branding) also released iconic sets for DBZ, Evangelion, Card Captor etc.
They are non-tcg pokemon cards, by the way and not non-pokemon tcg cards.
As for possible distribution of their counterfeits it was only in the same way that occurrs for the TCG - through dollar stores and alike. No licensed efforts. And there are of course many counterfeits and bootlegs of niche pokemon cards as people aren’t aware enough of what is legitimate or not.
Speaking to OP though. Most cards still have copies floating around out there and it does become a question of gradable supply as already mentioned.
Take for example the Carddass “Misty Wedding Dress” card (or Fan Service Misty card).
In the discussion in the first link I mentioned how “It seems to be becoming more sought after” and at the time there weren’t any copies on ebay. Fast forward to today and there are 6 raw copies and 1 counterfeit.
Now the condition of the cards themselves, such as this one, may not be mint but they have become available as resellers managed to source them.
The total PSA pop for the card was 15 (oct 14) and is now 22 (#23 Misty & Pikachu). If you made an assessment as to the scarcity of this card based on the surface supply at the time, you could have greatly underestimated how many exist. On the flip side to that, just because there is an influx of supply today of this card, does not mean it will always be available or in the desired condition.
And this is the main weakness when it comes to assessing niche cards. Because of their previous lack of awareness or popularity, it raises the question that if they were more popular, would that awareness bring more supply to the surface than anticipated?
My recommendation would be to just buy whatever makes you happy and at a price point that makes you comfortable. If scarcity is of great importance and you can afford it, then perhaps stick to items with documented print volume numbers, instead of unverified print quantities.
Just as an aside. Topsun cards aren’t generic either, but they are promo cards and should be in the same basket as the Meiji cards.