What is a proxy wedding

Where, when and why did the practice of proxy marriage arise?

I am answering this question using the material in the link posted by the OP. The interpretations are mine.

The power of attorney marriage originated in Europe in the Middle Ages. It was intended for 1) "power couples" such as kings and queens or very high-ranking nobles, 2) who wanted to ally but lived in geographically distant areas, and 3) who did not have suitable means of transport.

First, it doesn't seem to have been common (if it existed at all) during Greek or Roman times. In the days of these empires, power was in the "capital"; B. Rome or Athens, centralized, which meant that "power couples" consisted of marriages between the "boy and girl" next door.

In medieval Europe, after the collapse of the Roman Empire led to the creation of numerous and widespread centers of power, kings and queens felt the need to go abroad to find a suitable match. Given the "patchwork" of feudal stocks and states in Europe, the neighboring country may not be a good ally but an enemy, and a spouse with common interests (or enemies) may be someone from two or three countries. This would be a decision of the diplomats with the consent of the sovereigns. Perhaps one or both of them would be too preoccupied with war or other affairs to visit the other so that they would enter into the marriage (and resulting alliance) through a proxy.

In this day and age we have two “power pairs” but air, land and sea transport are so much better that they don't have the “pendulum” problems of European nobles. If anything, proxy marriage in America is for the LOWER classes, especially if the man is in the military or some other "wandering" profession and has trouble connecting with his intended bride.