Great topic.

It doesn't matter what the easterners think, not so much because they are in schism, but because their theology is generally useless. They have a very developed doctrine in the areas of asceticism and mysticism, but since they never enjoyed a Scholastic period their positive theology is pretty lame.

The non-sacramentality of episcopal consecration was the supposition of theologians for more or less the first millennium of the Church.

I think that this is a gross exaggeration.  If you think that Eastern Rite priests, bishops, theologians, etc. do not study St. Thomas and are unacquainted with scholasticism, you'd be mistaken.

Even among Western theologians, there is an opinion that bishops receive jurisdiction directly from Christ rather than through the Pope ... even if it's the less common opinion ... not that appointment by the pope (at least tacitly for the Eastern Rites) is not a requirement.  So, the thinking is similar to that about the Pope.  Church/Cardinals/electors select or elect the Pope, but Christ actually confers the authority or jurisdiction.  In the case of bishops, the Pope appoints the Bishop to his diocese, etc., but then Christ confers the jurisdiction directly to him.

As for jurisdiction being distinct from the Orders themselves, for long periods of time the two were never separated.  It wasn't until the consecration of so-called "Chorbishops" or, basically, auxiliary bishops, that you had bishops without jurisdiction in the Church.  In most of the Byzantine-family Eastern Rites, Chorbishops were eventually banned.  Really, one of the biggest reasons to have Chorbishops would be to assist with Confirmations, and in the East priests can confer the Sacrament of Confirmation.  Maronites, Melkites, and others continue to have Chorbishops, who are generally permitted to confer Minor Orders but forbidden (by law) to ordain priests (though ordinations to the priesthood by them would be valid though illicit), but you don't see them on the Byzantine Eastern Rites.

Even the etymology of "episcopus", meaning "overseer", implies the bishop being in charge of something, generally of priests and a diocese.  Some argue that there's a certain amount of authority inherent in the Holy Order itself even for bishops who lack appointment to a diocese or actual jurisdiction.

Great thread!

If you go to Alzog's Manual of Universal Church History (free online here: https://archive.org/details/manualofuniversa01alzouoft/mode/2up ), he discusses how the Eastern and Western theological traditions arose from different emphases in the theological schools from the earliest centuries:

p.260: "There existed a wide distinction between the two methods of treating theology, followed respectively between the East and the West.  The schools of the former preferred the speculative and theoretical branch of theological science, and labored to bring it into harmony with, and strengthen it by, the teachings of philosophy, while those of the latter seemed more inclined to develop the science in its practical bearing, and to bring out the legitimate consequences of traditional Chriatianity.  The former tendency was especially prominent in Alexandria."

He then goes on to discuss the catechetical schools of Alexandria, particularly those of Clement and Origin, so we are speaking of divergent theological methods/schools/emphases already manifest back in the late 2nd and early 3rd centuries.

On p.387, Alzog (discussing the Arian crisis) notes that, "While the Greeks, in more fully developing the relations of the Holy Ghost to the Father and the Son, steadily adhered to the wording of the Symbol of Constantinople, and, dreading that the Holy Ghost might gradually be made subordinate to the other two Persons, used the formula The Holy Ghost proceeds from the Father through the Son; the Doctors of the Western Church, such as Hilary, Ambrose, and Augustine, seaized with firmer grasp, and obtained a more steady view, and gained a deeper knowledge of the economy of the Triune God, and of the relations of the three Divine Persons.  These taught that the Holy Ghost proceeds from the Father and from the Son.  The addition of 'Filioque' in the Niceno-Constantinopolitan Formula of faith was introduced by way of explanation at the Synod of Toledo (A.D. 589), and is also found in the Symbolum Athanasianum.  This addition was the origin and occasion of most delicate points of difference between the Latin and Greek Churches."

It was these subtle differences in emphases, later evolving into subtle theological differences, which, gradually becomming evermore developed, would result in the schism.  Obviously, these differences grew/spread into other areas of theology, such as that ddiscussed in this thread.  The point of my post is only to show how far back -almost to the immediate post-Apostolic era- these divergences between East and West (and even within East and West) go.

PS: Alzog's is my favorite 2-volume manual of eccclesiastical history, and I highly recommend it.