I actually just found a pretty good metric to pretty much prove my point that Scholar is in fact lacking on healing.
The problem with looking at FFLogs to find the best healers is that the primary way FFLogs filters the "best" clears is that they sort by the length of the fight. Basically, the healers that appear on the teams that are highest up aren't the healer that heal the best, but kill the fastest. I don't think there's any dispute that Ast + Chain Stratagem will be a better comp than anything with White Mage at killing things fast.
But you can also sort to see the best healers and that list sorts by HPS, heals per second. Wanna take a bet what THAT list looks like? I'll give you a hint, there's not a single scholar on the list and it displays the top 100 classes. They are all Whms and Asts.
The best Whm had a HPS of nearly 6,500. The top Scholar on the other hand had an HPS of 4,250. Basically, White Mages and Asts are out HPSing Scholars by more than 50%
Now is this the best measure. Not really, I mean regens naturally out HPS shields, but still, by more than 50%? White Mages are Scholars are hard to compare because they really don't compete for the same spot, but given that White Mages are able to compete with Ast in regards to HPS it shows that in terms of healing that White Mage and Ast are relatively balanced (Though that may be an issue in itself since White Mage + Balance is pretty much going to beat White Mage 99% of the time in raid invites).
If Scholar didn't have Chain Stratagem I'm pretty sure all the comps would favor Whm/Ast instead. One of the classes needs to be Ast and Whm as mentioned before already heals as well as Ast, but does Sch heal as well as Ast atm. I really don't think so, the fairy isn't going to be enough to make up just the sheer potency and MP differences with their spells, and Asts shields are pretty much undebatably better though it's a bit harder to compare those 2 since you can't exactly filter by Noct Ast on FFlogs.