It wasn't the price but the cost of production. Most consoles are loss leaders. Also the lack of backwards compatibility made the library so small compared to PS2.
Dreamcast was muuuuch cheaper to manufacture than PS2. Seems Sega finally learned their lesson from 32x and terribly complicated Saturn. Too little too late.
The lineup of early PS2 games was pretty weak but yeah, back compat with PS1 helped them a lot. Dreamcast was surprisingly strong out of the gate as console launches go.