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I remember stumbling across something like this a while back on This Very Wiki. I had a look in the video games section of So Bad Its Horrible https://tvtropes.org/pmwiki/pmwiki.php/Horrible/VideoGamesOther
, in the Hardware folder, and I think what you're looking for is the Pro 200. Here's the commercial, complete with throwing the Street Fighter II cartridge in the trash!
https://www.youtube.com/watch?v=iF1n1AxK1Dg

Early 1990s, I used to see a commercial on television. It was targeted for parents. The product advertised was a handheld, battery-powered portable video game that had many pre-programmed games. I don't think it used cartridges or game cards or diskettes or anything like that, it was just pre-programmed games. The screen was a black-and-white dot matrix, I'm pretty sure about that. It was advertised to have a large number of games ("over 300 games" or something) but I was under the impression that they inflated that number by including variants of the same game. For example, remember Tetris? Remember how Tetris had "Type-A" and "Type-B" gameplay? According to this advertisement, those were two different games. I think Tetris was actually a pre-programmed game (or some similar kind of falling block puzzle game at least).
Now what really makes this advertisement memorable is that the (male) announcer tells the parents, "NEVER buy those expensive video game cartridges again!!" and the picture showed a close-up of a hand dropping a video game cartridge into a wastebasket. I particularly remember that the game shown was the Super NES version of Street Fighter II. As a kid, I instantly recognized it because I owned that game and it was one of the most popular games at that time. This means the commercial I'm looking for was probably aired in 1992 or 1993. Even as a kid I thought this was absurd, because I knew that game cost about $70 and the announcer described it as "expensive" so it wouldn't make sense for a parent to throw it into the trash, even if they bought a new handheld device with over 300 games.