As the other reply says, this didn't really happen this way. The Dreamcast was already on its way out after the PS2's launch by the time piracy really started up. Piracy was a footnote, not a cause.

Internet access was one constraining factor. Not everyone in 1999/2000 had broadband to download entire CD images. And an even smaller portion ever knew where to find the piracy methods and content - most of it was on Usenet.

I remember that the Dreamcast was already dead by the time piracy started becoming rampant, at least in the USA where I lived

Lack of a DVD drive killed the Dreamcast. People saw much more value in a PS2.

I had a Dreamcast at launch and still love the games that came out on it. If it had a new revision with a DVD player in it announced at the same PS2 price point to compete with the PS2 and XBOX then Sega might still be in the console business.

It really can't be overstated how important the DVD drive was for the PS2's success. When the first Fast and the Furious movie came out it almost seemed realistic that a criminal gang would risk their lives while attempting to steal DVD players from a truck. That movie's premiere was 8 months after the PS2 was released in the US. A DVD player AND a next gen video game console for $299 was an incredible deal in 2000.

PS2 marketing killed the Dreamcast.

Yes, this is far more correct. PS2 marketing had people believing that the PS2 was going to be rendering Terminator 2 level graphics in realtime.