Let's clear this up once and for all.
"It" is insulting.
To refer to a human being as "it" is to demean them, to label them as "less than human". Racists use "it" when the want to ultimately dehumanize their victims. Even in fictional or mythological settings non-human intelligent beings are always referred to as "him" or "her" even when gender is unclear or irrelevant. "It" means subhuman.
Applied to God this is even worse. You are referring to God as "less than human".
"It" is still singular, so it doesn't get round the singular/plural problem. Calling God "it" would still imply that he is singular in the exact same way that "he" does.
It is occasionally acceptable in English to refer to a multi-person entity as "it". ("This is the team. It plays football.") ButHowever "they" is much more usual. And this usage would strongly declare that God is three persons connected only organizationally, - to at least the same erroneous extent that "he" emphasizes the singularity of the Trinity - and is thus wrong to the same extent. And the usage would still run the risk of being taken as the deeply insulting sub-human sense of "it".
So in short 1. No grammatical benefit 2. Very insulting.
That's why it isn't done.