The difference there was that the Dreamcast could play burned CD-R copies unmodded, while the PSX needed a hardware mod to break the protection against that, a significant barrier to entry. Later it could be done with a plug-in to the expansion port, but early PSX mod chips required soldering.
The Dreamcast also came four years later, which mattered; many more people had broadband connections capable of downloading a full CD-ROM in 2000 than in 1996.
That said, I agree with your first point - Dreamcast piracy really only became a thing after it was clear it would lose the market battle to the other consoles. Piracy didn't kill it, at most hastened the death by a few months.
The Dreamcast also came four years later, which mattered; many more people had broadband connections capable of downloading a full CD-ROM in 2000 than in 1996.
That said, I agree with your first point - Dreamcast piracy really only became a thing after it was clear it would lose the market battle to the other consoles. Piracy didn't kill it, at most hastened the death by a few months.