Parents don't have children out of lack or need but because they want a family (at least that's the general idea).
I think the analogy you used above sounds fine.
Sometimes it's just a matter of how we say a thing.
If we say that it just pleased God to have a family, that works out fine theological.
If we say God felt lonely, or he needed a family, then that causes theological problems.
FYI, I've heard absolutely brilliant people misstate some of these things, because they just haven't studied, or thought about, these particular things.
The REASON I'm being so nitpicky about the "particular language" we use to describe God's purposes, is because that's a thing which leads to 2 really huge problems.
1. If we state God's purposes inarticulately, it can lead to all kinds of weird heresies based on misunderstanding God's NATURE.
(Most orthodox believers have a perfectly biblical understanding of God's nature, and I'm sure that includes you. But a lot of weird heresies come from getting parts of his nature wrong. So we need to be careful in HOW we talk about it.)
2. Atheists use this very issue to attack the existence of God, so this actually becomes an issue in apologetics.
Atheists actually bring this up in an effort to attack the existence of God. They first trick us into saying God created us out of a "need", then they show, with our own words, that a "need" shows a clear lack of perfection. Once they show God is "not perfect", and that our beliefs have internal coherency problems... they just keep going from there.
Hope you have a great weekend.