Dreamcast was released at a bad time, DVD components were still expensive so if they'd included a DVD drive it would have provided some future-proofing, but the console would have been even more expensive than it already was

There is no way they could have put a DVD drive and the necessary playback hardware in the Dreamcast and still sold it for a price people would pay in 1998. Standalone DVD players still cost $600-$1,000 back then. The argument should be that Sega launched the Dreamcast too early, but they were in dire straits and needed to replace the Saturn sooner than later. I'm not convinced they had much choice.

I think the PS2's success is a lot more complex than "it was a DVD player and a game console in one". The PS2 also benefitted from the massive amount of momentum built on the PS1, backwards compatibility, a better controller, and much faster hardware.

I was in my early 20s when the Dreamcast came out. The discussions online and amongst people I knew had a lot to say about the DC and PS2. Storage never once came up that often

It was always polygons. Sega was saying 3M (highly detailed and textured ones) and Sony was saying 66 or some ridiculous shit.

People were just waiting on it

Yes, by the time the PS2 came out DVDs were getting bigger and that definitely pushed a ton of people to get one as their first DVD player, since most were still over $200 so the ps2 was nearly free (fun point, that's how I convinced the lady I needed a ps3 in 2012)

But really it's about the marketing and PS2 hype. No one knew the Saturn existed, and it's largely due to everyone forgetting about them after the complete disaster that the Saturn was in the US

The lack of a DVD drive isn't what killed the Dreamcast. I'd argue that the nail in the Dreamcast's coffin was when software piracy on the platform became trivial.