Because it was! Trinitron was ubiquitous and found its way into every TV studio for monitors. Sony's heritage was pioneering tech and providing best quality, which warranted the premium brand price. Seems that now rivals have caught up and match with similar quality by are priced more cheaply, squeezing Sony's financial model, just as you say.
The area to compete now is services. Which Sony should have had up and running 5+ years ago. The had the best resources of any global company to establish themselves as the dominant digital content provider, with movie, TV, music, and game production. But they've arsed about and allowed themselves to be overtaken by the likes of Apple. If they remain just a CE device company, they can't really carry on as they are. They need that future service to become established. Or, failing that, some fantastic new technologies like Sony of old. Things like electronic paper and OLEDs have been Sony spearheads. I don't know that they can have anything new and exciting to rise to dominance like Trinitron though. There's way too many companies investing way too much RnD for anyone to likely get a massive leadership technology ever again.