I agree that as a monotheistic omnipotent god, Arceus isn't something that makes a lot of sense - but then again, I don't think it's meant to be a monotheistic omnipotent god, especially since even if we're just going on Sinnohan mythology, there are three other "deities" closely linked to Arceus - those being Dialga, Palkia and Giratina - and then the lake guardians, which also seem to have some relation to the creation mythos of Sinnoh. Rather than seeing Arceus as a sort of replica for, say, an Abrahamic deity, it makes more sense to see it as one of the many deities that exist naturally within the Pokemon world. Just like Alola has the tapus, which are worshipped, and Kanto has the mew species (I say species because it's implied that there are multiple mew), Sinnoh has Arceus and the other deities.
Looking at the dex entries for Arceus, it's interesting to note that nothing really paints it as being omnipotent - all it implies is that Arceus is at least as old as, if not older than, the "universe" - but that it created the world, not the universe. In fact, funnily enough, while none of Arceus' dex entries refer to it as a deity, both Palkia and Dialga's do. In that case, it's easier to see Arceus as a world-shaper rather than anything else - and to do that, it uses its plates, which allow it to harness the elements. In Arceus and the Jewel of Life, it's shown that the aforementioned Jewel was formed of the core elemental plates (and a few extras for good measure), so it's clear that Arceus uses these as a method of taking on power it otherwise couldn't have due to being a normal type, which further hammers home the fact that it isn't omnipotent, because it isn't a monotheistic god.
Though people in Sinnoh do build temples to Arceus in a way that resembles churches, that can be played off simply as them showing thanks for the creature that they believe gave them life. Arceus, however, isn't solely responsible for everything - it might have made the world, but if Dialga is the representative of time and Palkia is the representative of space, then Arceus clearly needed these to create the realm within with the world was formed. I also believe the idea that Giratina represents gravity, and that's a fundamental universal force too - but I won't go into that since I don't think that's canon. On top of that, mew is the possessor of all DNA, meaning mew must have been needed to properly form pokemon - and if we believe the Sinnohan idea that humans and pokemon are closely linked in terms of evolution, then mew is also responsible for human life, not Arceus.
These factors all point to one conclusion - Arceus can't be seen as a monotheistic god, and I don't think it should ever be viewed as such. Given that Pokemon is a Japanese franchise and the most popular religions in Japan are apparently Shinto and Buddhism, both of which are technically polytheistic, it makes no sense to apply Western monotheism to the culture of the Sinnoh region, especially since it's a Japanese-inspired region. To Unova, sure, monotheism makes more sense, but this isn't Unova. As such, seeing Arceus as part of a sort of "clan" of deities that also contains Palkia, Dialga, Giratina and, yes, several other legendaries, both from the Sinnoh mythos and from other regions, makes a lot more sense. Just think of Arceus as... the Zeus of them. Probably the most singularly powerful, but by no means invincible - and, like many polytheistic gods, not at all immune to death.
And at the end of the day, more than being a "deity," which is technically a human-created category in the Pokemon world, Arceus is a pokemon. "So-called god" is correct - Arceus didn't label itself that, humanity did. Just because we say something, doesn't mean it's true - but what is true is that Arceus is as much a pokemon as any other. Much like a poke ball works on a wooper, it will also work on Arceus - it's just a little harder to catch it due to its increased power level.