According to Catholic doctrine, the human nature which the name “Jesus” is associated with, is a finite creature. Additionally unlike other human natures, no human person inheres in it or acts by it; the personhood of this human nature is not human and proper only to a divine person, the Second Person of the Trinity. At the same time any action of this 2nd Person through the human nature is also done in union with the other two divine Persons as co-actors.
Why then is divine worship given to this human nature? There are two responses that can be made. One is that divine worship is primarily not to the human nature which is finite creature but to the divine person which is infinite. The other is that the human nature though finite creature nevertheless has a dignity proper to the infinite inasmuch as it is by the hypostatic union in close relation to the Infinite. In the final analysis, all that is appropriate to the worship of the Christ is nothing more or less than an acknowledgment of truth, the truth of the divine person who enters history through the Christian advent, the truth of the dignity of divinity which this human nature born of woman shares in by this Christian advent, and so on.
While I consider Catholic doctrine here to be elaborately conceived, its inelegance suggests that it, at mininum, falls short of truth perfect. In science, be it natural or philosophic, inelegant theories are disfavored because man knows the world is beautiful, knows the truth about the world must in turn be beautiful and knows inelegance is not beauty perfect. But the Christian revelation and doctrine is held to be perfect. So something there must be pruned, if not altogether abandoned.