I see your class right now is listed as BLM (well, THM, but at level 52 so I'm going to assume BLM) so I'm going to compare with that because I'm going to assume you have a reasonable understanding of that job.
On WHM the only time-sensitive part of our job we contend with outside of CDs on buffs/oGCD heals would be Freecure and Overcure, the latter of which goes unused more often than not. The only effect of Freecure is (as it sounds) making Cure II free to cast. Handy but by no means crippling if it falls off without you using it. It has virtually zero effect on our ability to heal and literally zero effect on our DPS. Two DoTs, an AoE or a single target nuke.
On SCH you may get the buff to make a Succor free (reduced? I don't even know, proves how integral it is I guess) when you use Sacred Soil. Everything else is a CD/oGCD on you or your fairy. No buffs to maintain. You get an extra DoT at least. It doubles as your AoE nuke though.
AST actually approaches something resembling a timer though since it operates exclusively off of RNG with very little ability for the player to manipulate results (basically all we can do is extend card buffs when they're good and CO/TD happen to be off CD) and only one DoT. One single target and one AoE nuke. Everything else is a CD or an oGCD heal.
Now let's look at BLM. I am no expert so BLM enthusiasts out there please don't hang me if I butcher a bit of this. First up we have Astral Fire and Umbral Ice, basic timers but already more integral to the class's effectiveness than any healer timer is. Ask any player with common sense and they will take a WHM who doesn't watch for Freecure over a BLM not paying attention to their AF/UI any day. The timers make the class.
Later on you get Enchain (sp?) which, again, if you don't cast enough during it you kill your own DPS. Even leaving out the new mechanics (with which I am even less familiar than the old ones, honestly the complicated buff maintenence and timers have kept me from leveling past 28) BLM gameplay is more technically complicated by 60 than any healer at 70.
I understand that healing is hard for some people. Some groups make healing hard for me and its my comfort zone. Just because its challenging sometimes doesn't mean it requires a higher level of technical ability.
Also for the love of god stop acting like healers are the only ones with basic CDs like AF to watch for. AF specifically even exists on a DPS class - SMN! Cooldowns and oGCD abilities exist on every class in the game, they are not specific to healers.