The Cases when EIP strongly needed:

More than one domain will be pointed directly to the instance.

We do not have a credentials to the access to the DNS for a domain / s pointed to the instance.

A instance need be available form the internet by IP. (As example any service interconnection by TCP from a other hosting location).

The Cases when EIP useless:

A Instance will be dynamically created.

A Instance used via ELB.

A Instance created by the Autoscaling Group.

A Instance no need be accessed from internet. 

The Cases when EIP may be not needed:

A Instance created for dev/testing/temporary purposes(depend to customer requirements, availability unused EIP's, etc) .