I wasn't under the impression that Bard was having a hard time bot.
His heal is in a decent place the last time i checked his values, especially when people level it as a last skill. And as far as his heal scaling from his meeps, that would be quite a difficult nerf to him as it would pressure Bard to roam a lot and collect mchimes to boost his healing and the heal value would overall had to be reduced because the potential power he could gain from it is big for Bards that make that extra effort.
Thresh's souls drop in his lane while Bard's chimes spawn in his vicinity - meaning he'd have to be absent from his lane a lot in order to use his scaling power efficiently.
All in all, if he'd receive the same treatment as Thresh and get 1+ HP for each chime, i don't know what his average chime collection is across Bard players but let's assume some numbers - 30 chimes on average and do the math:
#Caretaker's Shrine lvl 1, Bard has 50 AP:
Not charged shrine:
30 base + ( (50 x .3 AP) x 1.1 Windspeaker's x 1.1 Idol) + 30 = 78.15 heal
Charged shrine:
70 base + ( (50 x .6 AP) x 1.1 Windspeaker's x 1.1 Idol) + 30 = 136.3 heal
And then, you multiply this by 3 because 3 shrines are max. This looks like a significant boost to me just on lvl 1 ability and i am confident that i did the math correctly but i had to assume the number of chimes and his AP. Normally, in the beginning of the game he has at least half of the AP and no chimes so the actual values of heals are lower but consider the following that because of Spirit Visage as well ( Windspeaker's + Runic Armor + Arden't Censer + Mikael's) and % heal boost values stack multiplicatively with each other and on certain people, with certain items, stepping on Bard shrines may actually give quite a sustain, even more than they should get that also scales from Bard having more AP and collected chimes.
That kind of optimization is already available to Soraka but Soraka is missing CC and team mobility that Bard has. Currently he is a more popular champion than her and i generally see this as a problem as he may be able to compete with Soraka's heals with maxed CDR and optimized % heal increases.
Just my two cents.