Disregarding the 9700 Pro, really pushing yourselves here. Xbox came out in Nov 2001, but Geforce 4 Ti was Feb 2002.
The X360 was quite beyond what was available though, sans the resolution. And in handheld terms, the PSP was from the far future.
However both PS360 only made it possible by massive losses per unit and tons of R&D in custom hardware. Not something anyone at both MS or Sony aside of Kutaragi would want to try again. So yeah, it is possible, but likely the investment will be huge, and the price of the console will be evidently so, whilst still making a loss per unit.
That doesnt disprove my point that in the last double decade we have had a console launch that was more powerful than an affordable computer...in the Xbox case it launch with a chip beyond what was widely available at the time.
So in regards to next gen console, its is wholly possible for a next gen machine to drop with a GPU that is comparable if not better than an $800 computer.
A $500 next gen console should trump a midrange PC.
Assuming they keep up with the whole Premium and Reggie model....the next top box will probably launch with a chip that decks low-midrange computers.
The One X already gives a 1050/1060 a run for its money.
Next gen the consoles should have a problem beating the XX50 and XX60 of that generation.