1) Cordelia is the best flier in the game and possibly the best lance in the game.
2) +Atk is fantastic for her Brave Lance+ while numerous A-Skills make her easy to build.
3) As a flier, she has access to Hone/Fortify buffs for her, which launches her Atk and Spd alongside other Goad buffs.
4) Galeforce, when paired with Quickened Pulse (and buffs, but even without, some times), she can quad and activate it again to continue moving or strike another 4 times doing insane damage.
5) Galeforce, itself, is essential in top-tier Arena teams since its point-value is the highest among the specials. Equal to Aether.
You didn't get cucked.