"That's the problem with celibacy in the Latin Church - it is mandated."
Yes, it is. But consider it in light of all else you have written. Those men who should present themselves for priesthood are the ones who have already gone that far down the journey. Those who have not, yet, should work on their own spiritual state before seeking ecclesial office to shepherd others.
It is an extremely demanding standard, celibacy, for those still tied too heavily to the flesh. And it is precisely those who shouldn't be seeking holy office, but holy contemplation.
Jesus and Paul both recommended the celibate state. That the Latin Church has made that high standard THE standard, it seems to me, is an effort to put faith into practice.
We cannot choose to be good. We can only become good through faith and with the help of God, never on our own. Celibacy is something that will naturally follow as we approach the end-stage of theosis, as all physical passions, hunger, and corruption die, and the immaterial spirit defines us and overcomes our material prison.
Celibacy can be a goal we hope to attain, as a general overcoming of all bodily passions, but not a particular standard that one imposes as a precondition.
Celibacy, in its original and uncorrupted meaning is simply a vow of faithfulness to one's wife. The New Testament specifically states that a bishop would be a husband to no more than one wife, in other words -- celibate! It did not mean abstinence from carnal relations.
This original meaning then became corrupt and twisted to mean that bishops cannot be married, which is synonymous with not having sex with one's wife. In the Latin Rite, quite early on, celibacy progressively took on the meaning of a vow not to get married, for all priests, regardless of rank. Obviously that was not put in practice. For instance, St. Augustine was not celibate and certainly not free of carnal desires.
Even many a pope did not practice what the Church teaches, and engaged in carnal relations outside of marriage. Pope Alexander VI and his famous Banquet or Ballet of Chestnuts illustrate (no pun intended) my point.
Freedom from passion is a "natural" end-product of theosis. Expecting young, virile men who become priests to have reached that stage of theosis is unrealistic and reserved for a few saints.