First, the lack of an HD-DVD drive was a non-factor. As others noted, the increase in cost (both in losses incurred and MSRP) would have been astronomical, and it would have severely hampered the rapid early uptake of the machine.
That said, MS made two mistakes (and even these weren't entirely deal-breakers imo):
1. RROD
2. Not cutting the price more aggressively.
Beyond that, what is really doing them in is the out-of-nowhere success of the Wii--can you really fault them for not seeing that runaway train coming? Hell, I was *at* Nintendo HQ in Redmond the week before through several days after the Wii launch and I can assure you that even the people at Nintendo didn't ever, in their wildest dreams, foresee the current situation (yes, I include certain execs in that statement as well as dev people)--it wouldn't be an exaggeration to say that I was more optimistic than some of them and even my ballpark estimates were orders of magnitude off.
Also, bear in mind that while the PS3 is doing decently now, it will never equal the heights of the PS2 and, if Sony makes the same mistakes MS did vis-a-vis a lack of timely price cuts, they will find their installed base petering out as well. This is, of course, academic as the Wii is running away with this generation, so all Sony can really hope for at this point is a distant second place which is hardly something to crow about.
And think about this: if Sony had not shipped with a Blu-ray drive, there was not only the potential to ship the machine sooner but at substantially less cost (both in red ink and to the consumer) which would have allowed it, if not to match the Wii unit-for-unit, at least to have shrunk the gap a bit.
As it stands, its inclusion not only allowed Nintendo to open a mammoth lead but it also forced them to fight tooth and nail for second place in a space they expected to dominate. All this so that they could make a play for a market nobody is sure, even at this point, exists (right now it looks more like Laser Disc than the next DVD which is a helluva price to pay for crippling their gaming unit).