Removing Backwards Compatibility was the worst move Sony made...

[Millennium]

Since you're restricting the time frame to "since the release of the PS3" I can agree with you. I think they made worse mistakes before then, notably their utter failure to release decent dev tools for the Cell, but also depending on an immature and costly disc format (I see $599US as a consequence of this mistake, rather than a mistake in itself).

The PS2 had two major reasons for early success: FFX and the PS1 library. For some time, BC was that console's major source of good games. The same was true for the DS, PS3, and Wii at first, and it would have been true for the 360 too if its BC hadn't been completely botched. That's just what happens when a new console is released; building a good library of its own takes time.

The problem with the PS3 is that it cut off BC while it was still the PS3's major source of good games. They were using old and inexpensive hardware, and later on not even hardware at all, to implement BC. Yet they cut it off, ostensibly to save a few dollars, even though it's unlikely that the money saved by these moves was even significant. When you reduce your library by that much while failing to convince the market that what's left is worthwhile, you can hardly do anything but fail, and that is what the PS3 has done.