There's a slight problem. It doesn't 'effectively' achieve 2FA at all. If I lose my phone and lose my master key, I lose my all my identities, and even if I somehow remember them, I can't prove they are mine.

    HMAC(Master key + Domain)             -> private key + identity (public key)
    HMAC(Master key + Domain) + challenge -> response

Lose that master key, and you can't get anywhere. By contrast, FIDO U2F works loosely like this:

    1. first factor
    2. HMAC(Master key + Domain) + challenge -> response

Key point being that it's still 2FA, where SQRL is still just one factor. If you lose your FIDO device, at least as it stands, most sites make you have a token generator app as well, or at least a path through customer support.

It may help to think of an email + password as being two factors, and various 2FA solutions actually being three factors. Email is something you can prove independently of your password. SQRL has exactly one factor, and zero failover strategy.

It's debatable whether it should be possible to get through customer support after losing anything, but the 99% of online security infrastructure that builds a chain of trust upon your email address really does work for most people in most cases. It's terrible that email addresses are easily correlated across different websites, but the reality is that any replacement identity solution needs to be as easily restored in case of failure.

For SQRL to work and give you an out for lost master keys, it would need at least a way of creating a redundancy, like replacing HMAC(Master key + Domain) with an asymmetric negotiation of the correct identity, or adding another layer of indirection that makes the master key replaceable.