You could slow down the responses or rate limit the requests, with no need to completely block automatic logins.
I've just posted top-level in this thread listing two projects of which I'm aware that provide this, though as experimental protocols only. I've been mildly agitating for further development of such tools. Looks as if CloudFlare are working in a similar direction, which I see as positive.
IPs are cheap, if you let someone try 20 times in an hour before banning an IP, there are targets that people will cycle through IPs that quickly for.