Tough question ... to which I see two sides.
1. On the one hand, it runs several completely stable builds of ICS, and more GB + Sense ROMS than you could ever need. It is almost 2 years old, and is very much supported, and still has a strong dev community behind it. Those, are feats several new phones haven't achieved. Hell, its got stable ICS - the likes of the SGS2 doesn't even have that yet (even by XDA). So in this sense, no its certainly not dead - in fact its very much alive.
2. On the other hand, it does have a 1Ghz processor, an average camera and irritatingly low memory. And this does bring restrictions - it struggles with HD video, cannot run many games and is at times, sluggish. This, as in the Desire's physical and now nominally outdated hardware - I predict, will be its downfall.
So I guess, the answer to the question "is the HTC Desire dead" depends very much on how you use and what you want from your phone. If you want to customise it to the extreme then I say it remains one of the best devices for this. If you want your phone to be a showcase of power, I guess it wouldn't be the best choice.
Personally though, I think its far from dead. Dying, but a long way off dead