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.
By all means, use Argon2 in new code, or any other more modern KDF. But PBKDF2 isn't broken, and replacing it warrants actually doing the ground work to see if it makes sense: is it fast enough on most devices? is the security improvement meaningful enough? etc.
The truth is, 1password has the right idea here with their Master Key system. Even very unwieldy long passwords are pretty low entropy compared to a proper cryptographic key, and KDFs cannot significantly improve this situation. If you want to do more than re-inforce the speed bump, you're going to need to work outside the password. It has a usability trade-off of course, so maybe it's good that not everyone does it that way.