Good catch! I've added yet another option, you can enter the six-digit code manually in the "Check your email" screen instead of the magic link. This should cover this case without the need to enable password.
Found the use for it just now. At work I get my personal emails on my mobile device, but I am accessing textlog on the desktop. Getting a magic link on my mobile doesn't help me at all getting logged in on desktop. Enter the old, venerable, password.