As someone has said, it is impossible now to separate Christ from His human nature. Yet, the reason Christ took on human nature was for us to become god (theosis). It does not add anything to Him as a person because He is also pre-eternal God and it is His divine will which leads His human will. In our case, we are primarily human, yet, by following Christ we can become like Him through The Grace of The Holy Spirit (not by our own means which are not enough, as opposed to Christ who has life in Himself). This process of theosis continues forever, so we will always need Christ's humanity to serve as bridge between us and divinity. Also, we have a physical nature, so by nature we require a physical environment. For us, the spiritual comes together with the physical, that's why we can only be accomplished if we know God both as spirit and a body, whereas angels are content knowing God just as spirit (being only spirits themselves). Man has both the physical and the spiritual aspect; that's his distinction. Strictly speaking though, God does not need His physical nature for Himself, as there is nothing that can add or subtract from Him, but out of His infinite love for us, He desires to help and bless us in this way. Also, by becoming both God and Man, He proves that there is no barrier in the way of man becoming like God; man is infinite in potential.