What is the purpose of the spider egg hat?

The spider egg hat has no other purpose than the one you mentioned, which is to spawn a hostile spider egg 10% of the time. I will quote the Magicite wiki here on their article about hats:

"Its hard to keep up with the fashion in Deephaven. One not so popular trend is to put a Broodmother's Egg on top of your head despite it being very dangerous."

They have good reason for this! The hat is not popular due to it being potentially harmful.

Source: http://magicite.wikia.com/wiki/Hats

The Eggs can be used to farm exp to reach level 40 if you dont get hit long enough to gear up and farm exp.