The way I see it it's the other way around. The only complexity cost that lives here is that you need to distinguish between different derivation configurations. Whether that configuration tells you to use PBKDF2-200000 or Argon2-64M-4-1 doesn't matter, and you'll have to add a clause to the code either way. On the flipside, the memory-hardness allows you to increase the cost for the attacker a lot more than for the user.
> WASM Argon2 implementations are at least multiple times slower than native IIRC
I haven't looked this up, but my suspicion is that it's still better than a WebCrypto PBKDF2 configuration taking the same time for the user, measured in Wh for the attacker.