If I’m getting this right, you’re saying BIP39, which has 2048 words, from 0 to 2047, breaks into 11-bit chunks and matches that to the word list index?
Correct!
If that’s how it works, then I guess we could have our own word list, but we’d lose compatibility with existing wallets.
Correct!
I’m guessing if there’s a wallet that lets you pick your own word list, then you could use your own.
Yes! But note: you'd have to keep the wordlist somewhere safe too and this custom software needs to be available when you need it! So it's additional work and probably not worth it, since you can just cut your 12 or 24 conventional words into half and have 2 separate "factors" anyway; 1
Footnotes
You could use something more hardened, like Shamir's secret sharing, though I remember many years ago when I had C (HSM), Java (app) and Python (tests) development teams working on this for a secure system, their Shamir's libraries weren't compatible and this decision turned out to be max pain instead of max convenience, so maybe just stick with keeping things simple. ↩
Footnotes