I do not think we can draw, from Christ's humanity, a straight line to unfulfilled desire in God. To use this passage to develop an idea of "desire" in the Godhead blurs the Creator/creature distinction. I think those that jump here as "proof" that God desires certain things are ignoring the dual nature of Christ.Would you agree that God "desires" to see all men saved? Or that Jesus in his humanity desired to see all men saved (even though God did not will such a thing)? God is willing for all to come; but man's will is what prevents him from being saved such that salvationis 100% grace and of GOd, yet man's damnation is totally his own fault (Spurgeon's main point in the linked sermon).
I also think that it is appropriate that we desire all men that we meet to be saved. We plead with men to know Christ and don't make judgments concerning whether God has elected them. I think the "desire" is God's glory and the command to all men to repent. I don't think it's necessary to think of "all humanity" in the abstract and think: "I wish that God would save all men but that's not the way it's going to be." It is enough that, where God puts us, we strive with the men and women we encounter and plead with them to repent and believe. 2 Tim 2:24-25 is a useful passage that indicates compassion, concern, and patience toward men we meet. We don't exercise these things toward mankind in general but toward the men we meet.
I think the mistake that some primitive Baptists make is blurring the Creator/creature distinction and seeking to live as if they know God's secret counsel concerning certain men simply because they know God's revealed will concerning election. It proves the point that the Confessions make that such things need to be handled with great care - something some fail to do.