Herodotus said that there were more gods than men in Egypt, because of course the Egyptians regarded cats as gods.
You know, that would kinda put paid to the notion that gods feed on prayer and/or belief and die without it. How on earth would that many gods receive rites and honor?
You get something of the same effect with Rome. St. Augustine was ridiculing the pagans, but if his descriptions of the flurries and flocks of gods was too far off, he would never have gone for it as ineffective. (It's one thing to ridicule those silly outsiders for the in-group. But he was trying to ridicule them on their own terms.)
To be sure, it could be shown as having some effect. Ancient Egyptian magic involved invoking the names of gods, because to invoke someone's name gave them power, and the deal was results for power. Obscure gods were favored because they would be more grateful; the big ones got all the attention. Still, the god, ignored, unworshipped, still had power enough to work the magician's spells.
This is probably one reason why most fantasy polytheistic religions have so few gods.