Passwords are often already on the users phone. Such as if you use say Authy or Google Authenticator for your 2 factor, your phone if say an iPhone already stores all your passwords in your keychain which is accessible on your iPhone just like on your computer. Or if you use 1Password your passwords are accessible on your phone just like on your desktop. So still comes down to you having a strong master password for your keychain and or 1Password, etc that only you know.

If you use Authy on your phone, they have long had a chrome extension that allows you to get your codes on your computer, already for years and that works with all your existing codes rather than this which is limited to just GitHub currently it sounds.

But hopefully someone else can comment on the security improvements of Soft U2F or if its more just building a standard rather than people having to rely on Authy or such.