If I'm right, login with this method will be good, but it will hard to remember the signed message. Of course, we can make a backup, but we must save sign message to all of our device, in case we want to login in mobile.
You are misunderstanding.
If you just log in with the same signed message every time, then it is no better than a password (albeit a long and random, therefore strong, password). If some malware, phishing, MITM, etc., steals your signed message, then they have access to your account.
In eddie13's suggestion, the forum will provide you with a different unique message which you will have to sign every time you wish to log in. This system should also probably do away with the "always stay logged in" option, so someone intercepting a message once can't have access to your account forever.