I don't understand why the same logic can't be applied to お世話になっております
お世話になっております is not the same construction as
お V になる. It is originally from the phrase お世話になる or お世話になっている and may have a superficial similarity to
お V になる, but they are different. Some points to consider:
1. 世話 is a noun, not a verb. Yes, you can attach する to make the verb 世話する, but you still would not use the
お V になる construction when making it honorific. You would instead change する to なさる, as that is the appropriate way to make する honorific. Nonetheless it is more common to express this from the point of view of the person receiving the favor, as this emphasizes how indebted they are to be receiving the kindness.
2. The いる part of the phrase 世話になっている is changed to the humble form おる to become なっております. This keeps the phrase suitably humble, as it is the speaker who is being taken care of and thus なる applies to the speaker.
3. Third, since the other person is giving 世話, it is correct to make that word honorific by adding the prefix お. For example, if you told your wife you would look after the kids while she is away, you would not say お世話する, you would say 世話する as you shouldn't use the honorific お about an action you are performing yourself. *
*(btw that's meant as an illustrative example - I think there are better ways to say you'll look after the kids such as 面倒をみる).