As others have pointed out, the glaring problem with your analysis is that the PS2 had an enormous head start on the other two consoles, which the PS3 didn't have.
I'd add, however, that the problems from the PS2 (difficult/costly to develop for, too expensive for the consumer) are only exacerbated in the PS3: it's even costlier to program for, and it's twice as expensive to purchase. If the problems were just as bad as last time, one could claim that the PS3 would overcome them; however, the problems are almost twice as bad as last generation. This complicates things greatly.
Lastly, the most important evidence that you're wrong are the sales. Here's a chart of PS2/GC/Xbox sales:
http://vgchartz.com/hwcomps.php?cons1=GC®1=All&cons2=PS2®2=All&cons3=XB®3=All
Of course, none of these have their European numbers included, so this would actually be worse for the Xbox/GC if that were included.
Now, here is a chart of the PS3/Wii/Xbox360:
http://vgchartz.com/hwcomps.php?cons1=Wii®1=All&cons2=PS3®2=All&cons3=X360®3=All
Obviously, that chart is shorter and less complete, but you can't remotely claim that the PS3 is off to the same start as the PS2 was, compared to it's competitors. 6 Months after all the consoles were launched last generation, the PS2 had a near 15 million console lead. This generation, the PS3 is 4.5 million behind the Wii (and growing fast) and 6.5 million behind the 360 (and growing slowly). You can't possibly suggest that those are similar circumstances, can you?