The first thing that should be noted is that the legions weren't reorganized in the Byzantine period, they were reorganized under Diocletian in the 3rd century. The old legions were divided into two groups, "Limitanei" and "Comitatenses". The Limitanei were soldier farmers settled in the Roman borderlands, who defended the borders (Limes) and could be raised in emergencies, and the Comitatenses were the more traditional standing field armies. There were also the Foederati, "allies", who were non-Romans serving as mercenary soldiers alongside the legions. Outside of the organization, the tactics and weaponry of these legions were changing drastically as well, a consequence of a changing military meta. The gladius was completely replaced by the longer spatha and spear, rectangular shields were abandoned in favor of oval ones, lorica segmentata dissapeared entirely (though it had never been as popular as depicted in media), and cavalry was becoming much more important tactically. The higher organization remained essentially unchanged, though the quality of the limitanei declined drastically during Justinian's reign, right up until the Arab conquests of the 7th century. Tactics and equipment changed quite a lot during the 4th to 7th centuries though, with cavalry growing to dominate contemporary tactics, composite bows being widely adopted, the stirrup being imported from the steppe, and padded armor gaining popularity. Throughout this entire period, the lower organization remained essentially the same, at least in practice, with armies being divided into a hierarchy of consecutively larger commands.

The first real change in military organization during the Byzantine period came after the arab conquests in the 7th century. To secure the frontier and reduce upkeep costs, most of the surviving field armies of the empire were settled on imperial land, which they were expected to farm, in the Anatolian border provinces, transforming them into part time soldiers that largely payed for their own upkeep with rent and food from their farms. These soldiers had worse equipment than their standing army predecessors, but were largely organized in a similar fashion, though with an extreme focus on defense. Once the empire had secured some breathing room, the areas where these armies were settled were divided up into "Themes", military provinces governed by generals, who commanded the soldiers of their theme in the event of a raid or offensive campaign.

A standing force, in the form of the imperial tagmata, would be organized again under Constantine V in the 8th century. This was a relatively small, though higher quality, army stationed in and around Constantinople commanded personally by the Emperor, whose main purpose was to ward off potential rebellion among the generals. Military organization didn't change much, though the themes were reorganized into smaller units, until the 10th century. During this period, the Byzantine empire went on an extended conquering streak, and to assist this effort the imperial Tagmata were vastly expanded in scope and purpose. By the reign of Basil II in the late 10th century, the Tagmata made up the better part of the entire imperial army, at that point numbering somewhere in the 200,000's, and were deployed all over the empire instead of their traditional base of Constantinople. At this point, the thematic troops were being relegated to a support role as infantry, and would be disbanded entirely in the mid 11th century. During this period, the Byzantine empire had an army not dissimilar in command structure and organization to the old legions, though they used drastically different tactics.

In conclusion, the reason for the change in equipment was the change in the tactical cutting edge of late antiquity, and the change in organization during the middle period was the result of drastically changing circumstances, which was reversed once those circumstances changed. Why didn't the Byzantine empire use the legionary system, then? Because for most of the middle period it simply wouldn't provide any strategic or tactical advantage, and when it would it was essentially revived.