Chances are that you might not need so many healing abilities, and possibly more debuffing types, but I included what I'd run as a first test. Bridge officer abilities would be the main thing I'd change though. The skill build is heavy on evasion, mobility, and tanking type things because a dead healer = no healer, same goes for crowd control type effects.
For Doffs, I'd go with some that lower the cooldown on x-team effects.
For equipment, I'd test run with the Aegis set, not sure on consoles at the moment since I'm at work, but for weapons I'd probably use polarized tetryon beams and transphasic/chroniton mines or torps.
For the aft weapons I'm torn between beams and a torp or turrets and mines (turrets and mines for a more stationary arc, ease of use, and to take down target-able projectiles). Debuffing type weapons are probably the way to go since you won't be too heavy on damage, so slowing/DoTing or eating at shields seems like a good idea. The polarized tetryon beams have a 10% chance to eat at shields compared to 2.5% like normal ones, but the amount might be negligible if you're not broadsiding while healing.
Not sure how viable something like this is, but a if you're in a fleet that needs a dedicated healer it might be the way to go.
That would be pure healing though, and the thought behind the double team skills is the likelyhood that you would have to use them on yourself or on multiple people (redundancy gets around the cooldown issues for the most part).
"Practicality" doesn't really apply to a pure healing build, just like if you had a pure tank or glass cannon dps build. Its true that STO isn't usually played in a "role" fashion like most MMORPGs (such as a paladin class in this case, a true science ship would be more priest like), but it could be possible to perform that way with a group that was built with specific extreme roles in mind.