Primarily because Ken Kutaragi designed the most convoluted hardware alignment in history as part of a grand master "Cell" plan even when the original Cell project with IBM was falling flat on it's face.
A few highlights:
1. a substantial expansion on the PS2's already complex VU multi-processor architecture from having a core CPU + GPU + 2 VUs to something with a CPU cobbled out of two Cells, a GPU in the RSX that was effectively intentionally neutered to push people into using the Cells, then paired up with another six Cells. I like to think of it in retrospect as making developers play a secret game of Factorio they didn't know they were playing, in that they were expected to micromanage the offloading of tasks to all these various little factories, manage the return of the processed data, then find a way to tie it all together into an end product, all with an eye on not wasting clock cycles.
2. Divided memory architecture to make that 512 MB not universally accessible, so substantial data handling had to be planned for at all times (this was directly responsible for Bethesda's problems with the PS3 v. X360).
3. Very, very sparse code base, libraries, etc. to start with requiring large amounts of work just to get off the ground. Because you were supposed to be more directly controlling the process, not relying on middleware. But it was a generation dominated by middleware.
The end result was a PS3 that while meaningfully more powerful on paper than the X360 that difference in power and then some fell well within the "juice not worth the squeeze" category for 99% of all games made. Sony's first party studios went the extra mile and their products showed, but Sony ran an entire mythologized technical support team (ICE) to help their first parties and critical 3rd parties work with the system.
That was above and beyond the standard developer technical support they, Nintendo, and MS had always traditionally offered. They basically had a technical support rapid response SWAT team to make sure high priority titles didn't shit the bed.
Add the following:
1. The PS360 platforms were the beginning of western 3rd party dominance, a group largely more accepting of middleware and engine licensing than Japanese 3rd parties had ever been, at a time when the dominant engine on PC and the PS360 platforms was Unreal Engine 3, produced by Epic who was in direct partnership with Microsoft on the Gears of War franchise and had enough consulting input on the X360 to have the final allotment of RAM doubled specifically to optimize Gears and the UE3 engine.
2. MS had a one year head start so developers were already further along in getting up to speed on the new system.
3. The X360 worked with the DirectX API, further assisting the transition of development teams familiar with PC on to the platform.
Most of this was already mentioned in this thread. It's really best summarized as Ken Kutaragi assumed the Playstation brand was bulletproof so he and Sony management outside of SCE decided to use the Playstation as a trojan horse to push the Cell and Blu-Ray simultaneously. The belief was that we'd all have chips in our fridges, toasters, coffee makers, etc. before too long and with the economy of scale power offered by the PS brand that chip would be the Cell. Coupled with pushing Blu-Ray over HD-DVD, cutting the optical media license partnership from about 16 companies on DVD to about 8 on Blu-Ray (since the group pretty well fractured 50/50 on the next format).
On top of that they figured they could pass a good chunk of this additional cost onto consumers, hence the absolutely goofy MSRP.
Had Sony just pushed out a PowerPC based CPU with a more traditional style of Geforce 7 GPU using a shared 512MB of memory and the PS2 system on a chip they were pushing out in PSTwo's at the time as the OS manager they could have offered full backwards compatibility, ran on OpenGL and other PC standard APIs at the time to ease developer transition, and would have had backwards compatibility too, all while pricing 1:1 with the X360. Assuming they went with DVD as the standard media with a Blu-Ray player variant as the higher end version and selling a blu-ray add-on a la the HD-DVD add on for X360.
I'd make the same argument for Vita honestly. If they'd released a handheld with a standard LCD screen and based off a juiced up version of the PS2 SoC while keeping the form factor but branding it PSP2 they probably could have come to market below the 3DS cost with better visuals and maybe have made some real noise. But Sony got to Sony.