Right, it also would have split the user base, and offered absolutely no benefit to gamers using Blu-Ray, so 7.1 audio (or just great audio in general) that we all enjoy with PS3 titles goes out the window.
Also, it doesn't seem very likely that Sony would sell a player at $200, when the only profits to be seen from that are in royalties that will not be extremely large. Compared to gaming, where Sony can rake in profits from accessories, software sales (both disc based and PSN) and Blu-Ray (not to mention the videostore now).
PS3 + Blu-Ray afforded Sony the Blu-Ray victory, and probably cut their losses far more than simply launching cheap Blu-Ray players at a huge loss. Sure, Sony lost a lot on PS3, but I have a feeling they would have lost a lot more taking desparate measures to get Blu-Ray out the door at a cheap price, not to mention the "battle" for format dominance probably would have been a lot longer, which could have ultimately cost them more money. Not to mention studios may not have been so sure to line up with the BDA w/out the Playstation family support, at least ensuring millions of potential players out of the gate.
I think a lot had to do with the PS3 and it's install base, which contributed greatly to the success of Blu-Ray. The format may have won without it, but not as quickly, nor at such a "cheap" cost (not cheap, but perhaps cheaper than the alternative).