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) .