May I ask a potentially dumb question? Why store my password at all?
This 'idea' has been thrashed out a hundred times, even by supposed 'experts' like Egor Homakov who also says things like "You don't need 2FA, it's pointless and annoying for users".
The problem is, it is tricky to implement, a little bit old, and still vulnerable to bruteforce attack (Blizzard uses it, and IIRC their verifier database was leaked once, with g and N being published, so anyone could do dictionary attack on it. I believe Apple is also using it).
[1]: https://en.wikipedia.org/wiki/Secure_Remote_Password_protoco...
That said, the title could have been chosen more carefully.
Why can't they store my public key and authenticate me the way Github/Bitbucket/SSH all do?