Launched in 2006 with $500 and $600 price points due to being built around an expensive blu-ray player. The PS2 was still selling extraordinarily well. Sony could have saved themselves a ton of losses if they had waited until the technology became cheaper rather than burning through all of the PS2's profit by selling the PS3 at a substantial loss.
I knew the PS3 was expensive, but when you mentioned those other factors I agree.
Honestly if Sony didn't use Blu-ray and cell architecture for the PS4 they could sell it for hundreds of dollars cheaper in 2006. Heck, they might even still be able to cram in PS1 and PS2 backwards compatibility still.
Lifetime Sales Predictions
Switch: 125 million (was 73, then 96, then 113 million)
PS5: 105 million Xbox Series S/X: 60 million
PS4: 122 mil (was 100 then 130 million) Xbox One: 50 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima