If that happened, Heal would pretty much become an instant-cast massive heal - exactly like Holy Word: Serenity. That in my opinion would make it much too imbalanced, and would make Trail of Light a pretty much necessary Talent, killing the others in the row (Enlightenment is still sensible in Raids if you don’t play around Flash Concentration). Flash Concentration would also become much too skewed in power compared to other Legendaries.
10-time stacking Concentration would make it extremely punishing to refresh if it wears off for any reason. Right now in Mythic+ if you momentarily drop Heal at Prideful to kick in a Divine Hymn, the buff wears off if you go for Hymn’s full duration. If for any reason the 30-second buff wore off like that, there would be a ton of Mana lost in refreshing it.
Holy Priest’s problem is not throughput, I think. It can certainly pump big with little effort. Its problem lies in utility - no interrupt, no Combat Ress, no Self Ress, nothing like Ring of Peace or Roots, and no easily-interwoven damage that interacts with our healing. Sure, Restoration Shamans passed us in throughput. But I personally believe that more players will play Holy Priest if it got some things among the above.
A Prayer of Healing buff would be nice, though.