The Hero was a very solid first pick in Theros block Limited, as she was a one-drop that could easily become a 3/3 or greater quickly. But in Constructed, she proved to just be too slow for a deck that needed to rely on speed and mana efficiency. She was simply was too inefficient for Constructed Heroic purposes.
As it would turn out, Lagonna-Band Trailblazer from Journey into Nyx would prove to be a better one-drop creature as a 0/4 with Heroic for Constructed purposes. Also G/X Heroic proved to not be terribly competitive as U/W (blue/white) Heroic would. The best card G/X Heroic had to offer was Aspect of Hydra, which was played in Mono-Green and R/G Devotion instead (and still sees some play in Modern). Had there been more efficient Heroic creatures in Green, then this Hero could have had a good day.
Clearly, the designers of Theros block decided that Green Heroic creatures would start out inefficient, but gain multiple +1/+1 counters as they were targeted. This was fine in Limited, and this was even fun and very playable. (Setessan Oathsworn, for example, could become threatening in a hurry at common.) But in Constructed, creatures like Centaur Battlemaster and Staunch-Hearted Warrior were just too darned slow to be worth playing.
Hero of Leina Tower is a victim of not having the proper support, part of a case study in design creating an archetype that works well in Limited, but not in Constructed. The warrior was part of a feasible draft strategy that simply never functioned outside of draft and sealed play. When it came to building competitive Heroic decks, there were simply better options than the poor Hero.