I haven't played Sona much since her rework, so take this with a grain of salt. :P
Anyway, prior to her rework, she had fairly short cooldowns. It helped her build up Tear stacks without needing to wait very long for abilities to come off cooldown.
Nowadays, it just feels like her cooldowns are a bit too long to really utilize Tear's passive without just "spamming" abilities when they're off cooldown. Unfortunately, that could mean the difference between winning a fight and losing one because your abilities had another 2 seconds.
Rushing an Archangel's Staff could help, moreso for a Solo lane Sona, but it'd probably stunt Support Sona's growth and delay much of the utility she could be providing with Locket's shields or Zeke's extra damage instead.
Similarly, the longer cooldowns kinda hurt her usage of Sheen (though removing the AP on Sheen didn't exactly help either). I always enjoyed going Lich Bane and/or Iceborn Gauntlet on her.
Funny enough, if you built both Lich Bane and Iceborn Gauntlet, you'd get Lich Bane's damage and Iceborn Gauntlet's AoE Slow. Wonder if it still works like that..