I was simply listing historical attempts to achieve the subject of the OP - some were literal and "successful" and some were technical and philosophical failures. But there was NOTHING standard about them as generational divies and in fact both the 7800 and the 5200 roundly failed to provide sufficiently meanigful bumps compared to say, IntelliVision, ColecoVision or even Vectrex(which is kind of a sideways improvement).
I think there's lots of confusion here, or at least I'm not understanding how your point coheres. I was initially thinking you were pushing the Atari machines as iterative consoles like Scorpio, which they definitely aren't. You've now said your intent was just to mark them as analogous attempts to change the market. But how can that apply to the 5200, when Atari owned the market with 2600?
Similarly, I disagree strongly that the 5200 failed to manifest a generational leap over its predecessors. When I first saw 5200 games, they were mind-blowing versus the 2600 and Intellivision games I was used to. As you must know, comparison screens from multiple systems were a staple of game magazines and advertisements at the time. Even at those postage stamp sizes, Coleco, the 5200, and some PCs (as you pointed out) were clearly a separate generation. They naturally clumped into groups, helping define the very idea of such divides. (I suppose you could make the point that this kind of gapping wasn't yet "standard". But by the definition that evolved, it seems unquestionably to be a generational jump.)
The 7800 is admittedly much more like your description: a radical move meant to realign the market. But of course that market faltered badly enough that it never had a chance to even try, instead released too late, against too stiff competition. We can't know what its "sidegrade" hardware approach would've seemed like without NES or SMS to compare. But just anecdotally, I thought
Ballblazer was amazing looking, even in 1986. It was a taste of what PCs were doing in their space, better and more flexibly (as you were right to delineate).
And (one of) the original intent(s) of the 5200 was to BE b/c and it was shelved to create better marketing/tech distinction (you can buy an adapter that's more or less a physical adapter) as opposed to cost savings.
Isn't the 2600 "adapter" just like the Intellivision and ColecoVision ones, an actual separate console? I never had the 5200 version, but the pictures I've seen show controller ports on the adapter itself, unlike the 7800 with its true BC.