Dreamcast's strength was the hardware. Adding a DVD player would have just increased the price out of realistic range. The problem was the software and 3rd party support. The library just could not compete with PS1 and N64 and then the greatest console of all time came out and put it out of its misery, the PS2.
There's not really any one reason the Dreamcast failed, but the library being larger doesn't necessarily map to the library being better. The Dreamcast didn't have any heavy hitters on the level of a Mario 64, Mario Kart 64, GoldenEye or Ocarina of Time. In terms of games that are still in the mainstream consciousness, it's probably Sonic Adventure and Shenmue.
The library also had another thing that I think held it back from greater success: ports. Releasing so early, basically in the middle of the lifespan of the PS1 and N64, meant that a lot of the games were cross-platform with one or more previous-generation consoles. It's hard to demonstrate the power of a next-gen console when so many of the exact same games also worked fine on the consoles people already owned.
The other big source of ports in the Dreamcast library were arcade games. Sega was offering the ultimate in home ports of arcade games at exactly the time in the games industry when arcades were collapsing. The Dreamcast was the best way to play basically any cross-platform game that came out in that period, whether it was ported from arcade or lesser consoles, but ultimately they were games you could already play or that you specifically didn't want to.
I don't want to give the impression that the Dreamcast didn't have good or original games, it had both, just not "I must upgrade my console mid-gen"-quality games. It's a library that's aged very well but at the time, not enough people wanted what they were selling.
And part of the PS2's success was the built-in DVD player which was cheaper than non-console DVD players at the time. So if you were going to buy a DVD player anyway, you were better off buying a PS2, saving some money and getting a console at the same time.
Yeah I feel too many people overlook that in 2000 it was next to impossible to find a DVD player under $500 and then PS2 came out, lots if people who didn’t even game bought them because it was known for being better than anything even close to its price range.
N64 and PS1 have not aged well. I'd absolutely take a dreamcast over the N64 and the PS1 really only beats it on RPGs. If you don't have nostalgia for the 5th gen consoles, most of the games just aren't very fun anymore.