The only consistent complaints I've heard are that PF parties make everything hell (both from the side of healers complaining about party mitigation, and from others complaining about healers not keeping up with the bleeds). Meanwhile in coordinated statics, the primary complaint is that healing is too easy/predictable/reliable, and that becomes incredibly boring after the initial prog. Giving healers more interesting tools (especially damage focused ones) is the obvious solution for veterans in statics.
But I think it's equally important to recognize that PF healers are subjected to wildly different experiences based on their party members, and that what would be a hard healing check for a static becomes overly-stressful and possibly disastrous in PF. To put it plainly, tanks and DPS have too much control over the healing experience. If anyone messes up, healers have to res them and use single-target resources to top them up again. If there's a lack of mitigation (or even just inconsistent mitigation) healers have to compensate with more shields and GCDs to be safe. And if a healer dies (potentially not even their fault), recovery becomes incredibly difficult compared to a DPS death.
Let me elaborate. DPS jobs all have a 10% (or 5% in the case of Feint) mitigation at minimum. When combined, they can turn a 3600-potency heal check like Spark of Life into a 2800-potency one. Add in extra stuff like Magick Barrier, Curing Waltz, and RPR Crest heal and this can be as low as 2000 potency required from the healers. But of course, absolutely none of that can be relied on in PF, so healers often have to heal as if it's a 3600-potency check anyways. And that's looking only at the contribution of the DPS.
Tanks as well contribute 10% mit at a minimum, and potentially a heal+shield or additional 10% mit depending on the job. In a static, you could easily assume Reprisal is applied on almost every single raid-wide, but in PF this doesn't get discussed or coordinated, so it's basically a 50-50 on any given heal check. And the extra mitigations are, once again, completely unreliable.
On top of that, if you don't know your co-healer, there's another huge pile of question marks for "How much will my party cover for this heal check?" Too many question marks to list here.
Some of this variance is acceptable of course. That's just part of playing a team game. You have to coordinate your cooldowns if you want to have safe and efficient runs. But I think the amount of healing/mit that is out of healers' control is too much, with all the additional mitigation in EW (Feint buff, Magic Barrier on RDM, Crest on RPR, all the tank buffs), and considering how big of an effect they can have on the large heal checks this tier. The difference between an optimized static with a RDM+WAR, and a PF party where none of the DPS mitigate and the tanks use Reprisal randomly, is the difference between literally never using GCD heals, and using 1-2 of them on every single raid-wide and tankbuster (sometimes out of necessity, sometimes just for safety because you don't know what other people are doing).
For the sanity of PF healers, some of these extra mitigations and heals from DPS roles needs to be cut back or nerfed. And heal checks need to be decreased slightly to compensate. (It will still be harder in statics where the mitigation nerfs matter more.) I don't know if I would include tanks in that culling initiative, because I think a core part of their job is to mitigate for themselves and for the team, but I would at least take a look at WAR whose HPS can be half as much as healer when optimized.
And as a final semi-related point, I think healers suffer way too much when they die. The remaining co-healer has to rezz them and hold the fort while they get up, they lose most of their mana and resources like lilies, and weakness decreases their healing by 25%. It's too much punishment for an already punishing role. At least allow lilies and such to be saved through death.
TL;DR: If the devs want people to enjoy healing in PF, they don't need to make healing any easier, but they need to make it less dependent on random party members (and job balance) and less snowball-y when things go awry.