Taking out PS2 you get folks waiting for Emotion Engine sight unseen, take out Xbox as they came in thanks to the SEGA developments, they even worked together, so you just get GameCube which relied even less on the 2nd stick/extra buttons & came later with less than 500MB bigger discs
Anyway, many (most?) PS2 era top tier classics barely did anything with the right stick. From MGS to GTA, Final Fantasy, Resident Evil 4, Wind Waker, Twilight Princess & Metroid Prime, the Dreamcast would have been fine with such games/genres/styles and successors to its RPG, fighting, racing, sports & arcade games. Maken X controls like Metroid Prime. If folks wanted Halo-like T/FPS, they'd have the choice of an eventual twin stick controller (PS had no trouble making it its new default with few real/good dual analog games) or mouse & keyboard, though PS2 beat Xbox with little of it.
Even when you need more buttons, you more often than not still have the 4 (8?) d-pad directions as back then it used to be available as alternative to analog controls or even do nothing while nowadays it's very commonly used as additional inputs (ie weapon/items in Souls) so it could have been used for things like items, menus, actions in MGS & Zelda type games where people say you totally need extra shoulder buttons, on top of other clever still decently intuitive stuff like hold L then tap R to toggle stuff one way, hold R then tap L for the reverse, etc. Personally I'm also partial to the old GoldenEye/Perfect Dark single stick defaults as with the right gameplay it's weighty and physical like controlling an action game character in FPV, auto aiming what's roughly ahead Doom style (or lock on like Prime) and precision aiming RE4 style. I liked the option in later FPS like TimeSplitters. Though games like MDK2 were great with the face buttons as WASD, left stick as look/aim, L to jump/glide/jetpack/whatever, R to shoot and the d-pad to switch and use weapons/items/scopes/gadgets etc. Sure, after 25 years it's the reverse of what you're used to but it worked and works
Not that PSP isn't proof enough, it has identical inputs (worse analog) and did just fine from Monster Hunter to God of War to MGS to GTA to Final Fantasy to Syphon Filter to SOCOM to Daxter to Resistance to Tomb Raider to Medal of Honor to racing to (S/J/A)RPGs to fighting, sports and more.
And yes I know about the claw grip crap but that was way over the top and unnecessary for sane folks, I played Monster Hunter a TON on that system and just momentarily tapping a direction for my character to face that and then tapping the camera button to recenter it (or even moving my thumb from the stick to the d-pad during long animations) was more than enough and became second nature, in the heat of battle or not. Though the series later made it so the recenter button just faced the boss monster (and in PSO there's automatic flying boss camera etc.) so, it's all design
Edit: I forgot about 3DS having the same controls (its FPS tended to use the touch screen for aiming, possibly to their detriment sacrificing other inputs, but other games didn't). So the DC died in 2001 but its controls survived in Sony to 2011 and Nintendo to 2017 proving it wasn't the issue. Of course I don't claim the stick didn't have many great uses, just that it wasn't that big a deal just yet considering you could still have some of the greatest games of the whole generation doing little with it, and plenty others that did more could have been tweaked like them without it being so weird!
Idk about the space, it seems enough for epic RPGs like Skies of Arcadia, maybe they'd focus less on FMV doing stuff real time like that instead if they wanted to be on DC, even Grandia II has some of the in-engine stuff on Dreamcast done in (meh) FMV on PS2, the GTA III port has fit on a CD-R, Vice City would fit on a GD-Rom etc. I didn't think changing discs was a big deal, it was done a lot on PS, PCs had tons of install CDs and it wasn't overdone on Dreamcast and could have probably been trimmed with less duplicate files (it helped loading) etc., the max was like 4 Discs for rare games like D2/Shenmue 2. Voice acting and FMV was mostly for the highest end games, your average JRPG didn't have as much as Square's to think they would all need a ton of discs for the Dreamcast to have the genre or anything, most like the Persona or Tales of series would probably be on just 2
I'd have probably enjoyed it if it lived on but got different types of games because of this rather than be like current gen where every system gets the same stuff in slightly different performance/resolution. Like FFVII started way different on N64 and turned to something else to utilize PS discs too. Of course I'm not defending their decision to not take the Saturn 3D Control Pad which was better if they were gonna go with this design. Maybe they were being Nintendo-like in an approach trying to simplify things to attract non gamers like Nintendo with Wii for example, it could have worked. It's not like DC died over a lack of games, it got tons and fast, so, had it lived on, even with mainly SEGA support with successors to its varied catalogue tuned to its hardware and whatever third parties could fit their games without many discs, that would still mean a pretty meaty library for us all.
