Healing in WoW Classic was great. I played a Priest during that time and I remember some things very clearly, such as:
-DON'T OVERHEAL. This was pretty much rule #1.
-Make downtime for yourself. This was the era of the 5-second rule.
-DPS can continue to DPS with 1% HP. If they aren't in danger of dying, don't heal them.
-Efficiency spells like Renew and Greater Heal are staples. Flash Heal and PW: Shield are for emergencies.
This was an era where it was completely possible to WAY overheal someone. Casting Greater Heal at a Rogue was probably going to produce 1-2k overheal even if they were at 10% HP; the right answer was to throw that Rogue a Renew and for the Rogue to step back for a few seconds to bandage.
You could even overheal a tank if you were not careful. The best way to heal was to keep Renew running on the tank and be "casting" a Greater Heal while watching the tank's HP carefully. If they got a series of dodges or parries then you canceled the heal so you could stay out of the 5SR (5 second rule) and keep regenning with 100% Spirit.
Now healing was definitely abusive in WotLK. I won't argue there, but you missed the mark going into Cata.
Healers no longer have a mix of efficiency and emergency spells. Instead they have ONE efficiency spell and then an array of spells that, while not necessarily suited for emergencies, are very inefficient.
Let's examine the Resto Druid, since a Druid is what I am playing right now:
-Lifebloom: a great heal-over-time that can, for whatever reason, only be placed on one target at a time. It's not incredibly efficient, but it does have good throughput when stacked and can proc mastery and buff Nourish.
-Renew: A highly inefficient heal with a short cast time that has very low throughput thanks to having its healing split between a direct heal and a very short heal-over-time. Procs mastery and buffs Nourish.
-Nourish: The Druid's "efficiency" spell. It is a very modest heal with a long cast time.
-Rejuvenation: A very modestly efficient heal-over-time. Procs mastery and buffs Nourish.
-Healing Touch: A slow-casting, modestly efficient direct heal with excellent throughput.
-Wild Growth and Tranquility: Area-effect healing. Not suitable for any other purpose, but excellent in those roles. Only efficient if healing many targets.
In this lineup, one thing should stand out: a dramatic lack of "efficient" healing. There really is only one go-to spell for efficient healing, and that's Nourish. However, Nourish happens to be the absolute least flexible spell available to a Druid.
There is no danger of overhealing at all. The heals are too small and even the very powerful Healing Touch will not heal for more than 20% of a DPSer's 100k HP. There really is no decision to be made here, and the typical Druid tactic of healing predominantly with HoTs and only using direct heals when they get behind simply is not sustainable -- partly because Lifebloom can only be on one target and partly because the other HoTs are far too expensive.
Edit: I left out Swiftmend, but the main points still stand, given Swiftmend's long cooldown and general inflexibility.