I don't think that's true. Going back to apophatic reference, we can say that the reason why G-d is not a basketball is because a basketball has properties whereas G-d doesn't. Something which lacks property can't be similar to something that has properties.
If you want to argue that lack of property is a property, I guess I'd have to agree, although that doesn't seem very coherent.
This reminds me of the via negativa/apophatic approaches of the Middle Ages of describing God by what God is not (though I know divine simplicity has earlier roots). I think there are several good reasons to reject simplicity and to reject pure apophatic approach (two different things, but with similar counterpoints and rebuttals):
1) Regarding the via negativa, describing something solely by what that thing is not has two problems.
a) If you never say what something is, you can't even get to say the thing exists (if you do, then you're getting around to assigning it properties)
b) Negation is still a limitation: not being a basketball is still an instantiation of logical identity, specifically excluded middle: A v ¬A ("A or not-A").
2) Combine this with criticisms of simplicity.
c) Reasonably we should be able to be univocal with things we refer to: we can only do this with properties. If we can't do this with God, then it means that we run into absurdities, some unintuitive, some analytical: we couldn't say that God has the property of being "the referent of the reference 'God'," which is absurd. We couldn't say God has logical self-identity, which is absurd. We couldn't say God has the property of existence even, as mentioned above (Kant fans will say "existence is a predicate," not incorrectly; but Kant only means it isn't an
essential property)
d) There are surely some properties which you would assign God: for instance, is God a person? That's a property. Is God powerful? That's a property. Is God wise or knowledgeable? That's a property.
e) Classical simplicity has it that God is identical with God's properties (to get around the idea that God "has" or "possesses" properties). However this must be pointed out as being absurd: if God is identical with God's properties, then those properties must be identical with each other (if a = b and b = c, then a = c). I'm not sure if you're arguing this far into simplicity, but there it is anyway, just in case.
I think it's inescapable that if God exists at all that God must have properties, because to exist is to exist as something -- and to be something is to be
that thing rather than something else, and that entails having properties (limitation) demarcating what that thing is from what that thing is not.