Q should be stronger in best-case scenario simply because it's harder to achieve; same reason as skillshot should deal more damage than a targeted ability. Not everyone is going to auto attack; that squishy, long-ranged AP mage ain't risking their ass for a measly 60 bonus damage.
To better understand how weak her auras are, let's compare them to similar abilities.
Q: Since there aren't any other direct AoE AA empowers, let's check out an ability that is the opposite: Tryndamere's Mocking Shout. It removes 80 AD from each person on enemy team - and has much bigger AoE, therefore making the best case scenario easier to achieve. If every person on enemy team AA's once, that's 400 damage lost right there. Of course, as I said, not everyone is going to attack - but, unlike Sona, Trynd isn't limited to a single AA. It is likely that just an ADC will fire 4+ shots in those 4 seconds - making for a 320+ damage loss on a single person. If it affects an enemy AD jungle/top it has outdone Sona's best case scenario by a large margin.
...oh and it also comes with a big-ass, non-decaying slow. Completely fair and balanced ability. /s
W: You can't compare an AoE shield's total value to a single target shield. To make it more fair, compare it to another AoE shield - Karma's. It shields for a total of 1200 + 300% AP (double the base and 3 times the scaling), while being ranged, having better AoE and a non-decaying 60% MS boost - so it is not only a better Sona's W, but also a far superior Sona's E at the same time.
E: 1% MS per rank. Enough said.
I honestly don't see why should Sona feel like shit outside of a best case scenario when people mentioned above and much more get to feel useful regardless if they hit 1 person or 5 persons. Maybe it is a combination of auras and unavoidable poke - but then again, Riot obviously has no problems with LB nuking you from a screen away and blinking back before you can retaliate.