Davies already hit this, but adding on: the situation is often either "forced" upon deities after a certain point (e.g. they used to have enough power to create things and exist independently, but that power has waned/disappeared or been expended/taken away, and now they need to replenish it) or is a natural step in the "evolution" of a deity over time. E.g. deities are "born" in some way that doesn't depend on worship, but after they "mature" they require it. Forgotten Realms took the former path, with Ao the over-deity (a different class of being from regular deities, regardless of power) punishing the gods by making them dependent on mortal faith--taking away their self-sustainability. (As others have shown, the whole thing in FR is pretty fraught, so what exactly this meant isn't clear, but something changed and deities became at least more dependent on faith than they used to be.)
You saw something kind of like this in Egyptian mythology, coupled with the "natural life cycle of deities" stuff I mentioned above. E.g. Ra eventually retiring to his solar barque full-time because he's become too old to be a "living" god anymore, and had lost the faith of most mortals, while his father Nun (one of the really obscure Ogdoad) remained a nigh-omipotent but not particularly person-like entity/force/being. This was also used in various places to explain pantheon syncretism or the addition of new gods, whether by adoption, division of an existing god, or divine reproduction: the old gods dying off to give way to the new.
Yeah, it's...pretty much just the idea of constructivism applied to belief-shaped magic, and then deriving from that maltheism, that any so-called "gods" that do exist are inherently bad and wrong (because they deceive people into worshiping them) and deserving of nothing but scorn. It's a pretty old and tired trope at this point, since (as others have said) you can see examples of it way back in the 30s, and it was commonly used as early as the 60s with original series Star Trek, both played straight (the ep with Apollo) and tweaked slightly (the multiple episodes with powerful D&D-god-like computers that rule over societies forced to remain at primitive tech levels, e.g. Return of the Archons and The Apple).
While I'm not going to steal this idea proper, I'm totally going to riff off it for my DW game. Thanks!
I've long thought it would be entertaining to roll it back just a little further than that: Divine High School. Bahamut as the golden boy in seminary and Boy Scouts among other things, with his hyper-rebellious sister Tiamat barely avoiding expulsion. Kord and Moradin as the guys in shop class--Kord because he's not-quite-delinquent but really just doesn't mesh well with organized schooling, Moradin because he's a military brat who's big on the whole "self-sufficiency" thing. Everyone knows Ioun is valedictorian, though she's got big competition from both Corellon and Asmodeus (though everyone thinks the latter's got some secret advantage). Etc. All sorts of great sibling drama, relationship drama, politics, factions...it's pretty much perfect, you'd just have to find some way to integrate the whole "worship and devotees" angle.
As said above, they often don't care, or aren't really capable of noticing something as small as mortals. If gods are to us as we are to ants, then these super-gods are to us as we are to molecules. Too small to see, too small to really care at all about, even if theoretically they're important to us in some way, we could lose trillions and never notice.
Dreams can be powerful things though, even IRL. They can motivate entire nations. If a dream could have sapience and willpower, and grant magic to others, how much more could it achieve? And if these dreams can exist for thousands of years, continuing to gain knowledge throughout that time, who's to say they couldn't be epic? Remember, our epic context doesn't go any further back than about 4100 years (the Epic of Gilgamesh, ca. 2100 BC). There's no reason a deity couldn't have existed for double that length of time--far longer than any history humanity can trace.
Deities are often more problematic for being too powerful than for being too limited. Limits on divine power are generally desirable to a designer.
I, personally, am always up for cosmological discussions, but I understand if you don't feel it appropriate for this context.
A mindless process is usually inert once it's finished--or needs a reason it's not still doing the same things it did to start with. Mindless processes also have the "okay well...why did that mindless process happen?" infinite-regress problem.
"A being who dreams all the other stuff into existence" is, more or less, the same as the aforementioned "primordial chaos deities" (like the Ogdoad, or the Greek Khaos, or the primeval underground fresh-water ocean Abzu/Apsu in Babylonian myth). It's a little more complicated than that, because (as noted) Ra is able to talk to Nun in some way, and receive things from him. But there's still an idea that these beings in some sense undergird reality in a much more abstract, and indeed dreamer-like, fashion than any of their deity "children."
