X-inactivation is a little bit more complicated than that. While the process of X-inactivation initiation is random, once a cell has settled on one chromosome, all its daughter cells will silence the same chromosome. The initial process happens in the early embryo, so large patches of the body have the same X chromosome silenced.
This pattern is visible in some animals. E.g. a tortoise cat's pattern arises due to the hair color gene existing on the X chromosome. Consequently, male tortoise cats are rare (XXY, XXXY etc only)
Statistics would indicate that that is a plausible scenario.
In addition, a uniparental disomy can occur as well. Here, the X chromosome was duplicated in the egg cell. So the exact same X chromosome is inherited twice.This is an error in meiosis. This could occur in XXX (with the third X from the father's side), XXY, or even XX. That latter one would be rare, for a uniparental disomy on X without a third sex chromosome would mean both egg and sperm cell had an error during meiosis.
You could also see a single X (Turner Syndrome) as a 100% dominant X-chromosome. But that may be semantics.