A body in a theophany is like a mask. A temporary manifestation. The smoke of a flame.
But the body of a human nature (such as the incarnate human nature of Jesus, or our own bodies) is the normative, healthy, best, proper expression of the nature.
Disembodied humans (in the intermediate state between death and resurrection) groan for their bodies. But Deity itself doesn’t groan for a body.
When Christians say, “God the Father doesn’t have a body”, we aren’t denying the possibility of the Father using a body in a theophany. We are denying that he needs a body for the normative, healthy, best, proper expression of his divine nature. We are also saying that any body used (whether in theophany or in incarnation) is itself created by God.
In this light, Joseph Smith’s First Vision need not imply that the Father has a human nature (no more than the Spirit’s appearance as a dove implies the Spirit being a dove). Indeed, I doubt that it did for the original recipients of the 1835/38 versions of the account.
For the modalist, it could imply simultaneous manifestations of one Person.
For the classical Christian adherent of the Trinity, it could imply a simultaneous theophany of the Father, and a christophany of the Son’s permanent incarnate human nature.
Mormonism makes big assumptions about God in interpreting the 1838 First Vision account to imply both polytheism and the Father’s essentially human nature. These are completely unnecessary and go against the Book of Mormon itself (which is strictly monotheistic).