Leading armies doesn't necessarily make one a good emperor. And Irene accomplished quite a bit. She lost support because legitimacy was very important to the Byzantines, and she was not legitimate - and murdering your own (legitimate) son is not a way to win public acclaim. Compare that to Zoe, who was the legitimate empress, and who was the most utterly incompetent ruler in Byzantine history, but was beloved by everyone.
A competent and legitimate empress would have been formidable.
Comparing Anna with Zoe, though, is a comparison that simply doesn't work. Zoe was the last surviving member of a dynasty that had ruled for nearly two hundred years, and the niece of the greatest Emperor in centuries. Moreover, she was popular with the populace precisely because of her very incompetence- the fact that she wasn't allowed anywhere near the reigns of power by her various (underrated) husbands meant that she could become a convenient rallying post for all who were dissatisfied with the current Emperor, and wanted an easy way of getting rid of him, by trumpeting the legitimacy of the Macedonian Dynasty.
Anna, on the other hand, is the elder daughter of an aristocrat who himself came to power in a coup. The establishment of the Komnenid dynasty is still well within living memory, they don't have the huge span of time that membership of the Macedonian dynasty gave to Zoe. She'll have come to power violently, as Anna did, by killing her legitimate brother, who was reasonably popular with the citizenry for his benevolent and pious nature.
There is no doubt, in my mind, that an Empress Anna will be capable and ambitious- but then, so was Irene. Irene's successes were remarkable- she reconquered half the Balkans, and came very close to achieving the restoration of Constantinopolitan sovereignty over Rome. But she totally lacked popular legitimacy, and so will Anna Komnena.
EDIT: Regarding the issue of reconquering Anatolia, after the First Crusade, it dropped quite quickly down the Imperial list of priorities. The Sultans of Rum were seen as Imperial vassals, and thus part of the Roman Empire anyway, by Constantinople: and furthermore, they were generally rather more reliable as vassals than were the Hungarians or Crusaders. Much of the Komnenid period is, in my view, better understood as a succesion of campaigns to slap down uppity client states by the Komnenid Emperors: as opposed to a long, grand programme of systematic reconquest. In any case, the Empire did very well indeed without the Anatolian plateau: economic growth in the twelfth and thirteenth centuries was higher than at any point since the sixth.