From Yato-no-kami on Wikipedia:
The Yato-no-kami (夜刀の神?, "gods of the night-sword") are snake deities in Japanese folklore appearing in the Hitachi No Kuni Fudoki. They lived in Namegata county, in fields near the government office. They were rumored to bring familial extermination on anyone who saw them. Eventually, they were killed by a man clearing the fields, enshrined, and banished to the mountains.
This might explain why Yato does not have a shrine and since. Since Yato-no-kami exterminate people, this might also explain why he is considered a god of calamity. AndIt would also explain his snake eyes.