Will it really disrupt the pattern of the universe if the gate is left open? If you have an animal that will escape or animal intruders (we used to have heifers and a Shire horse eating our garden if we didn't) if it left open, then OK, put a sign (available at most hardware stores) saying please shut the gate... if not, then what the heck....

If you really don't like to see the untidy gate swinging in the breeze, letting the fresh air blow through, then get a spring closer as mentioned above.

Now someone find a song about it and everyone will be happy.

LTS