This is my first thread on GAF, so go easy on me.
Not a bad first thread at all, OP.
I agree to a large extent that Cell did help shape Sony 1P into what they are today. Not so much on the tech difficulty side: PS2 had some VERY esoteric hardware itself and was quite difficult to program for in its own right. However, PS3 was the first gen where a Sony console was difficult to program for AND a competitor had a "perfect storm" console in terms of ease of development, proper timing, strong technical performance, proper funding, great features innovation and a growing library of strong exclusives as well as great marketing, in the form of the Xbox 360.
With the PS2, systems like GC and Xbox beat it in a lot of technical areas and had a good stable of great exclusives (in time), but they released way too late to be much of a factor. They didn't really have good timing or stable of exclusives to go up with the onslaught PS2 started to see starting with GT3, either. As for Dreamcast, it came too early, and lacked proper funding after the initial period as Sega were bleeding money. It was much easier to develop for than PS2, but came up short tech-wise in some key areas, namely geometry and lighting (you can see where some of this comes into play with even early releases like GT3 vs. Le Mans on DC; check out that Digital Foundry GT retro series).
Because 360 satisfied a lot of those aforementioned conditions, combined with the complications of early PS3 development (and manufacturing, which affected the pricing), a LOT of 3P devs either finally decided to seriously support Xbox for the first time or, in some major cases, released massive AAA games on Xbox exclusively. If not that, 360 got a lot of DLC content early or exclusively (COD comes to mind), and was often the lead platform for 3P games. Even a lot of Japanese support that was once exclusive to Sony started to do a lot of work on Xbox with the 360.
That forced Sony to more or less revitalize the PS3's brand image on their own, and with maybe a small handful of 3P support along the way (like Konami with MGS4). Their 1P teams had to innovate with IP and leveraging the PS3's hardware advantages, and in time, they did. So teams that were already quite good, like Naughty Dog, elevated a lot higher than gen due to those circumstances. Some other 1P teams didn't quite elevate as high as they could, like Polyphony, but they were able to still see some gains and help with restoring the PS3's image as well as show off what the system could really do.
PS3's issues are also what forced Sony to take the path they did with PS4 and, building off the momentum PS3 had from 2010-onward (especially since after that point, 360 more or less gave up on the core gaming audience with their 1P), helped PS4 incredibly well off the bat with 8th-gen. So while I think PS3's hardware was a definite factor, it wasn't the only one, or the main one, IMO.
Toshiba was making a pixel shader only focused GPU with gobs of eDRAM for it (CELL taking over the vertex shading duties… innovating but also taking the PS2 design and turning it up to 11, you can see where they wanted to go), but yes it was ditched for RSX at the last minute and got a bugged chip too.
Their approach could have worked had MS not launched early and with such good HW performance (and architecture) and SW support.
PS3, due to some issues, ended up feeling like less than the sun of its parts for a while, but devs who tamed CELL ended up liking it a lot.
A huge benefit with 360's GPU were the unified shaders. Even if Sony went with the earlier approach (which I haven't had a chance to hear a lot about, but its sounds very interesting and could've been really cool given the great technical performance in games PS2 provided for its time), they still would have lacked unified shaders, so it'd of always been a "limitation" in comparison to 360.
Putting that in quotes because, again, it would come down to how devs used the hardware. OG Xbox had a few graphics pipeline advantages (again regarding shaders) over PS2, but PSP's hardware was robust enough to work around that plus at the time devs hadn't completely became acclimated to that newer stuff to the point where it seemed difficult to do similar results on PS2.
Maybe could've been a bit different with PS3 vs. 360 as unified shaders did become a big part of PC shortly after 360's launch, and the 360 gen is when a lot of PC-centric devs and franchises started pushing hard into the console gaming space (they were already making waves here and there the prior gen but Japanese studios ruled the roost for the vast majority still), but you never know.