You would need (counts on fingers) 0000, 0001, 0011, 0101, 0111, 1111 reversible dials for a four-shaft loom disc, I think (or 00, 01, 11 half-dials, or 0, 1 quarter-dials).So it’s doable, printing one disc per warp and having a stable socketing mechanism. It’s going to be bearing the compression force of the warp tension into the outer peg or inner shaft of each wheel, so your locking mechanism will end up having to provide resistance to separation — lego pegs won’t be enough. Twist-locks would work in one direction but tend to separate in reverse, so you’re better off using a hollow center core with alignment pegs to stabilize the 4-way 90° inter-discs and then using a rod with a cotter pin holding on a crank wheel at both ends (that provides the grip to rotate it against the warp tension).
So, for a 40-thread you’d need 240 discs; or 160 plus a handful if you conserve on the 0000 and 1111 discs as specialty / edge-only. Plus a rod, two cotter pins, and two grab wheels.
Binary wheel storage starts to become a problem. If you construct wheels out of 0’s and 1’s you can store simpler parts, though probably at a 25% discount on end quantity (or better, depending on how you budget for all 1110/0001 or heavy use of 0000/1111 not). Or you can use wheels with dowel sockets and put metal pins into them that lock into neighboring discs when assembled, which would benefit from having the crank wheel be stable to set the tower upon during assembly.
None of this even remotely fits within the level of simplicity of production, storage, use that the 40-thread pattern bar provides at a $20 price point. You’re better off printing your own solid pattern bar as they do, if simplicity of use is a concern and you have the skills and access to do so; but if you distribute that pattern bar model or print, you’ll collide with their patent, since you haven’t materially innovated in the above disc-and-lock system ways, so plan for a licensing payment to them if you intend to distribute a solid pattern bar.
(Thanks to the video game Shapez for teaching me to think about 4-tile assembly in terms of rings rather than circles.)
ps. I still want one of these quite a lot.