Two writers who have produced 'global' hypotheses about the features of polytheism are Jean-Pierre Vernant and Walter Burkert.
Vernant identifies the following features:
A god is a power that represents a type of action, a kind of force. Within
the framework of a pantheon, each of these powers is defined not in
itself as an isolated object but by ...
Part of the problem you are having lies in the way you are framing the issue, i.e., where you say:
The worshiped gods [...] require the care of humans worshiping them at
their "houses" (temples) on earth
You've inverted the relationship. Gods do not need the care of humans on earth; humans want to appeal to the power that gods ostensibly have, and ...