What happens to gods with no regalias? What happens to gods without a regalia? I am writing a blog and want to know for details. I know Yato mentions it but i can't remember!
I don't think this as been addressed in the anime, but I imagine gods have to fight off things to stay alive and uncorrupted. Remember that purple painful skin after a god touches a monster? Well, that needs to be avoided.

Without a weapon (regalia), if fast enough, a god can just run away or dodge attacks to avoid any danger. Yato was pretty strong on his own and his opponents were surprised by his personal abilities on multiple occasions.

But it is a god's duty to protect the human world (Near Shore) from the creatures of Far Shore, and only running away makes them pretty useless for this cause. Bad creatures will be left to trouble people and other gods, which might result in bad reputation, and furthermore additional hostility from gods and humans. People's prayers would not be answered (at least those involving bad creatures) and remember that "supergod commitee" which got pretty pissed off at one point and tried to destroy a fellow god for doing what they thought was wrong without investigating too much. Wouldn't wanna risk that.