Most of the time there isn't much point/benefit in using the first battle sprite skills as it doesn't provide much benefit compared to 2nd or 3rd abilities.
Simply put, make battle sprites passively use their 1st ability (without putting the other two on cooldown) on the nearest enemy from you and drastically reduce their cd's so they are able to fire them off at a constant rate; Drakon could be one with shortest cooldown due to the primarily offensive nature, followed up with Maskeraith and Seraphynx being on the more supportive side (range of those could be between 3-6 seconds respectively).
This adds a lot more value to the sprite in general and adds a lot more value to the Ultimates themselves, particularly ones with a more offensive nature like Meteoric Firebolt/Virulent Quills/Dazzling Light Ray.
This would also add a lot more value to harnesses as higher tier ones would be a straight DPS increase for sprites and there would be a lot more benefit in using the other damage type harnesses as well.
Needs to be a toggleable thing as well; sometimes it would benefit not killing off mobs to prep for next wave in an arena, or you just want to have a moment to admire something, etc.
I have to strongly disagree, Maskeraith's and Sera's first ability are very strong and Mask alone defeats the purpose of having a poison weapon/vials/barriers alone, with positive DPS outcome, and Sera is particularly good against Slags in FSC, and turrets, you can improvise a lot with Seraphynx alone, too.
I'll say the better approach is to buff Drakon's Fireball, as even pressing the "1" button and holding «Attack» will charge your weapon and use it's ability, still giving you positive DPS, since it's slightly faster charge time instead of shield spamming or charging the weapon normally.