Think about it another way.
PS2 vs. Xbox.
One was a custom designed piece of hardware that was very hard to extract performance out of. The other was an easy to develop for piece of hardware using common desktop PC technology.
In general games looked significantly better and performed significantly better on the Xbox. Obviously, all the games were on PS2 because that was the dominant console not because it was the better console.
Sure the argument can be made that the Xbox came out a year later, so it has a technology advantage.
So, in games that were playable on both consoles, Xbox generally gave a much better user experience.
PS3 vs. X360.
Well, the PS3 came out a year later than the X360, so the X360 can't lay claim to releasing later with an advantage. Instead we should be saying that PS3 should have a technology advantage since it launched later.
Very different hardware architectures. PS3 is significantly more powerful in many ways but is also significantly harder to program for. X360 had some advantages and disadvantages as well, but it was significantly easier to develop on.
Hence, the vast majority of multiplatform games looked or performed better on the X360. Sure if you could afford the time and effort to try to extract performance out of the PS3 you could get some pretty good results. And towards the end of the generation multiplatform games on PS3 started to look and perform as good as they did on the X360. Not because it intrinsically suddenly became easier to program for, but developers could now use shared libraries that made it easier (but still not as easy as the X360) to develop games on the PS3. Basically the closer it got to X360's ease of development, the closer it got to matching the look and performance of games on X360.
Sure, 1st party developers that can afford to spend significantly more time attempting to extract performance out of a difficult to develop for piece of hardware could do some really nice things. But everyone else who didn't have that time? They were basically releasing worse versions on PS3 of games that were released on X360. And that only started to change as they got access to shared libraries from those 1st party developers.
So, which would be the better design from an end user POV? The one that starts out looking and performing well right out of the gate compared to the competition and basically still matches it at the end of the generation? Or the one that looks significantly worse at the start of the generation but can finally match the other by the end of the generation?
Neither PS2 nor PS3 are making a case that custom hard to develop for architectures are better for either the consumer or the developer. Generally speaking the easier it is for a developer to create something for a platform, the better the end user experience will be.
As such, Sony decided to follow Microsoft's lead, not only because custom hardware is expensive and requires you to have far more expensive to employ engineers on your payrol, but also because they were increasingly losing developers to the Xbox ecosystem (by this, I mean developers were choosing Xbox as the primary development platform due to ease of development). And that also creates it's own advantages that will be experienced by end users. Primary development platform means games released for it will have more time, polish and attention to ensuring it runs and looks well on that platform versus other platforms regardless of any hardware differences.
So, as such, had Sony stuck with custom hardware, even if that hardware was significantly more powerful than hardware that shared common technology with PCs, the vast majority of their games would at best have looked and performed similarly to a less powerful console using PC technology and at worst would both perform worse and look worse due to the difficulty extracting performance from the custom hardware.
Now, is custom hardware more interesting than PC derived hardware? Yes, because it's an oddity. And oddities are always interesting. Could it be more powerful? Quite possibly. Would that potential power translate into most end user experiences on that hardware? Well, history tells us that no, it wouldn't when compared to a relatively similarly performing piece of hardware using slightly customized general purpose PC hardware. At least not until the ease of development started to approach the ease of development of using slightly customized PC hardware.
Regards,
SB