Piracy was just as rampant on playstation 1 and just like the dreamcast, it didn't require the use of a modchip. Piracy did hurt the sales a bit (on the PS1 too), but it's definitely not why the console died.
The dreamcast issue is that no one wanted it. I was the only kid with a dreamcast in my entire school. The playstation won the previous console wars and the marketing surrounding the playstation 2 and its "emotion engine" (which in retrospect was full of bullshit and edited CGI) was so insane that it convinced people to wait for the PS2 and made them disinterested in anything that would've been released before it. You could say, Sega was already dead by the time they released the saturn as there were already very few people looking forward anything they'd make. People felt screwed by all the mediocre genesis peripherals (barely any game worth owning on megacd and 32x), the saturn did terrible, it's a miracle there was enough life left in Sega to even build the dreamcast.
Nintendo could've also died during that time period. It's only through the sheer strength of their first party titles that they could retain enough of a niche to survive. Something Sega didn't have. Sonic has never been their own Mario. They never had their Zelda or Mario and they didn't have much third party support beyond arcade developers. That really doomed the DC. EA refusing to make games for it didn't help. They tried to strongarm Sega into letting them be the only sports game developer for the platform, Sega refused and EA said they wouldn't develop for the platform then if they weren't given a monopoly on the genre.
With no strong first party games the kind that makes a ton of people buy a console solely for their sake, and with dropping third party support, the DC's sole niche was fans of arcade games, just like the Saturn. That's an extremely small niche. I still play arcade games to this day and thus keep up with the news in the genre and it's getting difficult for the specialized companies like CAVE to survive. They're now focusing on mobile games.. companies like Degica help retain the genre on lifesupport by porting the old ones to Steam but there's not much in terms of newly made games nowadays.
It certainly was in the Mega Drive/Genesis era. Sega dropped the ball between the Mega Drive and Saturn eras. Too many poorly-supported extensions to the Mega Drive (Mega CD, 32X), Saturn was apparently too hard to program for (especially for 3D games), those things are what appears to have damaged their 3rd party support the most.
As for Nintendo, I'd say Pokémon was key for them doing well in the early 2000s rather than Mario.
" the marketing surrounding the playstation 2 and its "emotion engine" (which in retrospect was full of bullshit and edited CGI) was so insane that it convinced people to wait for the PS2 and made them disinterested in anything that would've been released before it."
That's what happened in my area. I fell for it, too, esp as MGS2 was the game I was following and their people could actually deliver on that marketing a bit in gameplay demos. Little did I know that it was going to be quite the exception. :)
"It's only through the sheer strength of their first party titles"
What I just said to ZenoArrow. They didn't have strong, original, genre-defining content like Sony and Nintendo did. Microsoft was careful to avoid that mistake.