I don't think the lack of dual-stick killed it.
Many factors play in:
* Mostly the piracy killed Dreamcast. It was way simpler to copy the GD-ROM than the Xbox and PS2 DVDs.
* The lack of DVD functionality, which both Xbox and PS2 came with.
'Piracy killed the Dreamcast' is very commonly put around, and it was incredibly easy for a contemporary console (literally just burn a CDR, no hardware modifications required), but if you look at the attach rates [1] for the console, they are comparable to successful consoles. Pirated games still needed consoles to be played, so we would expect a much lower attach rate than normal if this was a primary factor.
Ultimately, it was almost everything else going against the console. [2]
Yeah, this is the common refrain after the fact but it wasn't as easy at the time as people think, the ability to just burn a disk and go on a stock Dreamcast came pretty late in the lifecycle. And this is 1999 and 2000, it's not like literally everyone was on Facebook and sharing tips on how to burn disks. Heck, even the internet connection large enough to successfully download disks at all, and the hard drives to easily store them, weren't that common. In 2022 optical media is clearly inferior on the density front to cheap SD micro cards, let alone other storage techs... in 1999, even a single CD was a whackload of data and hard to deal with. Not impossibly large, but it's not like it is now where you can lift a couch cushion and find a 8GB sd micro card you forgot you had, and then throw it away, because what use is 8GB anyhow?
I think the more conventional marketing discussions are much more relevant. In an alternate universe where Sega hadn't burned the entire market with the Saturn, but simply released the Dreamcast at the same time otherwise, it may well have done much better. I'm not sure there is any way it could have "won", while I have my quibbles with some decisions in the PS2 hardware it is generally superior enough that it probably would have won anyhow, it might have been a more grinding war. (Bear in mind that part of this alternate universe is better support from the gaming companies because they weren't burned and they still had some residual good feelings about Sega remaining, so the DC would have been going in with more high-quality games in this version of reality.)
The simple truth is that six months into the Dreamcast's run in the US, before any of the next-gen competition had emerged, I could just tell it wasn't in for the long haul. The library was just too lopsided and the support from the big names, while not entirely absent, just was never there in the necessary quantity. The competition actually coming to market merely buried an already-dying console. But it's the only console I've ever purchased on release day and I didn't ever regret it. There was a lot of good and interesting stuff... there just wasn't enough.
But the performance was outstanding in Dreamcast.