I asked the question because "actual hardware" is ridiculously vague and pretty inconsistent with respect to how much power is enough power and in what areas. You're right that it's mostly the thing that seems to matter but there's no yard stick to decide how much is enough. We can see it with the CD-I. Compared to the Genesis, the CD-I has a faster processor, more RAM, can push tons more colors, etc. So what makes it not powerful enough to kick off the next gen if hardware is the primary concern?
And like I said before, when it comes to measuring hardware capability, there's no agreed upon standard. We see it whenever somebody asks if the Jaguar was really 64 bit. You'll get different takes on it based on different criteria for making these measurements and different people give more weight to different aspects. The Intellivision was 16 bit but nobody seems to suggest that the Intellivision marked the beginning of a new generation the way the PC Engine is said to despite the PCE's 16 bit-ness being the primary reason for starting the new gen. Where's the consistency?
It seems to me that the generations are measured based on a relatively arbitrary calculus that accounts for hardware capability, time period (hence why the crash somehow factors in), and whatever marketing gimmicks may have been in play at the time. I guess its good enough in a pinch to give an idea of what a particular decade was like but we may as well just say "early 90s gaming" or something and it does the same job. Or simply be specific enough to say "Genesis gaming." I don't see why we bother numbering the generations. Especially since once we start hitting double digits its going to be completely unwieldy.