WHM's current design shows that this is really not the case, and that a GCD-heavy healing style CAN work, with certain design elements (that being, the damage is refunded later). If SE went all in and made WHM into 'the healer with multiple tools that are GCD but refund their damage later', then it'd carve a new identity for the job: that of (at high optimization level) being able to bank those refunds, and unleash them all at once during the Presence of Mind window for a massive-impact and satisfying 2min window. It can retain it's ease of use via how upfront bursty its healing tools are, how it can respond to big incoming damage with 'I have Cure 3, try me', and how it has quite good mana economy now (thanks to lilies now effectively giving you 1600mp per minute saved, plus Thin Air).
It could have even further 'ease of access' changes that wouldn't 'simplify the fun out of the job' with things such as having Medica upgrade to Medica 2 (given that Med2 is equal potency to Med1 after a single tick), and alongside that, a trait that 'halves the cost of Cure 3 when Medica 2's HOT is active on the WHM', bringing it from 1500 down to 750 per cast (making Cure3 the new 'spam this while you've got the HOT ticking if you need extra oomph' skill). Plus it opens a hotbar space for something else to be added, to counter those who would argue 'hotbar bloat, so we can't have any extra damage buttons' (we can also do the same and have Cure 1 upgrade to Cure 2, to get another slot freed up)
In the current design, that is the end goal, though. To heal entirely using OGCDs (or for WHM, OGCDs and Lilies which are damage neutral). If that's the 'only way to give healers DPS rotations', then we should already HAVE those DPS rotations. We also should not be designing around 'well maybe people will be selfish in PF'. I've played in DF and ended up with people who don't have their job stone on purpose in 50+ dungeons (for RP apparently). I've even had to, back in HW, coheal a Savage with one. We got the 'big hitboxes' thing in response to people complaining about uptime issues, and I think it's primarily because of Tanks in E6S being forced to have like 5 GCDs of downtime with the tornado soaking part. There's plenty of ways for people to be 'selfish' that aren't 'healers greeding for their barse', I've equally seen Tanks or DPS wipe the group because they gapclose in too soon for their mechanic and get everyone killed. But that's acceptable, I guess, because it's their role to do damage. Oh wait, it's not, for Tanks
Please make it make sense
Oh also, if you have extra skills (with CDs/DOT durations) added to healers, those skills will be higher potency than the filler, so as to make them get used. Thus, interrupting your 'rotation' to heal would actually be less punishing under such a system, as compared to now, because more of your skills in your timeline will be 'not filler'. Any time you have to heal and lose damage because someone ate orange pancake, you would lose a filler cast (eg a Glare). Going back to ARR, SCH's damage mainly came from it's DOTs. Ruin, it's filler at the time, was a mere 80 potency (with it's DOTs being 240, 350 and 300 respectively). Of course, if someone wants to barse, they should shut up and join a barsing PF, instead. Trying to barse in random PFs and taking it seriously like that is a fool's errand, and they have nobody but themselves to blame when they complain about 'someone ate damage and ruined my barse'. Your barse was ruined the moment you joined the PF, not the moment you watched Johnny Samurai get clipped by the AOE.