As others have already stated. It's very common in MMOs for DPS to have to manage their aggro. If you meant that it's not common to see a DPS pop threat reduction in DF dungeons then I can see that being mostly true yes. Doesn't mean they're in the right, it's just that for the most part enmity generation for tanks is pretty easy in FF14 so it's not often that you have to use it, hence it isn't a go to.
The DPS in your example is totally wrong for complaining to the tank though. He should be managing his own enmity.
How do you measure effort? If you want 100 comms it's less effort as healer or tank. If you mean how much effort went into clearing content.... it's a little hard to measure as everyone will have a different opinion. Some people find DPS hard, others tanking hard or healing hard. DPSing for me is way more effort for instance.
Honestly though, most of the content in ff14 is pretty easygoing on the healers. Especially ex roulette stuff. A bit of stupid is barely a dent in the process, not anywhere as penalizing as a squishy tank for example.
That's because tank and healers are much harder to balance. Not only is their balance complex because if you up one aspect of their kit it has the effect of uping/nerfing another aspect of their kit as a result (give a healer a stronger heal and his DPS could potentially go up from not having to heal as much). But also because changes to these classes can also affect the damage output of the rest of the party (better mana management or mitigation could outright change strats and dps output).
And lets not even mention synergies between healers' and tanks' mitigation and healing kits.
Because of this these classes really need to be homogeneous to avoid serious imbalances.
Also there really isn't anymore pressure. The only pressure you have is not to die because your death could be hard or impossible to recover from but that's about it. Yes some responsibility is transferred to healers mostly. But with greater responsibility comes greater power, you also get to pick who gets to live and who dies because you can't be bothered healing stupid.
Overall I don't think tanks and healers are abandoned because of any of this rather than it being due to every kid wanting to be a virtual badass and healer/tank isn't really that.
That's not true. Mana is a huge liability for DPSing as a healer in plenty of content. Dungeons and aoe DPS particularly. A dungeon party with low DPS is a HUGE HUGE HUGE Mana drain for the healer even if there is ZERO damage to heal. Caps for emphasis because I cannot stress this enough. If your party takes forever to kill packs of mobs you'll burn through your mana management tools in no time by just DPSing. It's much easier on the mana being in a party where the DPS is high and everyone is standing in aoes.
The other two things that can drain your mana are raising and overhealing.
It's extremely rare to have mana issues if dps is good, nobody dies, and you don't overheal much (<30%). Sounds like a captain obvious statement but what it means is that stupid is rarely a big hindrance if stupid survives. Classes like BLM are pros at "surviving stupid" but a lot of players use moves from their books if they feel like the healer has their back and it comes at very little expense on the healer end.
I'm not saying DPS mentality isn't a thing (it is for very good reason, namely game design). I'm also not saying it doesn't suck. It very much does if people are dying right and left for that .5%. It's just that everything becomes easier with more DPS and if people being stupid for that sake is upsetting, it's even more upsetting getting people who have no clue what they're doing, have low dps and/or non-optimized characters that you need to carry around like dead weight even if their mechanic handling is flawless.
Pick your poison, basically.