Firstly, I don't think the situation of 'you didn't use your auxillary DOT, reported' happens remotely as much as implied (mostly because you can't report someone for 'playing wrong'), but also, even if we were to assume that it IS an issue, it has a similar solution as multiple other 'issues' of people not doing good damage as a healer: incentivize dealing damage, make 'doing damage' more accessible, and make 'losing damage because of something getting in the way' less punishing. Lilies are a good example, previously, good healers and not-so-good healers had wider disparity, because the good healers could work effectively with their cohealer to minimize the number of GCDs used on Medica 2, and not-so-good healers would lose more damage to Med2 casting. Now, they don't lose as much damage, because Misery provides a refund while allowing healers of all skill levels to do their job, of healing.
One of the big problems with the current formula SE's lumped healers with is how few damage buttons we have. But what I mean by this, is that to deal good damage, we have to press our filler spell. Every GCD that is not the filler (or DOT refresh), for ANY reason, including healing we're forced to do (eg safety shielding as SCH/SGE in prog) is a massive damage loss. We've seen in other threads that in ARR, SCH's Ruin spell was a mere 80p. It had 3 DOTs to put up (Bio, Bio2, Miasma), and those were a bigger source of their damage, with their total potency per tick being higher than a Ruin cast. What this meant, in practice, was that while it's higher complexity to manage 3 DOT timers, the 'punishment' of having to actually press a heal was way lower by comparison. Now, if a SCH has to use a shield, instead of losing 80p, they lose 295. Our effective 'punishment per GCD' has been vastly increased, because all of the potency that was spread across multiple skills keeps getting piled into the few that we have left. If we lost the DOT, for example, then Glare would get even stronger, making 'missing a Glare' (eg movement) even more punishing.
Please try to look at it from the point of view I'm looking at it from: that our kit as a healer is divided into two distinct halves: healing, and damage. I want to incentivize these healers with 'less damage' to be able to get 'more damage', not by removing 'wrong choices' from the kit (as has been tried by SE), but by incentivizing the 'right answer'. If we have, for example, a gauge that builds by doing damage, which can be spent on a damage-neutral heal, it incentivizes the player to try and do damage to charge that move up, and use that to cover healing required, rather than fall back on Medica spam. Then, if my whole idea were made real, that heal is then refunded by gaining access to Quake, Flood and Tornado, further incentivizing the player because these new moves look very cool and powerful. The player is incentivized to deal damage (when safe) to charge up to the cool heal (which provides cool damage moves), and rely less on Medica1 spam. Additionally, SE has said that 'they didnt know what to do with SCH' for EW, which apparently resulted in Expedient. I think that if they were open to healers having more damage buttons and interactions, then they'd open a lot more space to work with. SCH attacks that build Fairy Gauge, AST attacks that cause Minor Arcana to come back faster, SGE attacks that augment Kardia healing in various ways, etc.
I won't say 'it never happens', I have seen it, and more than once. But it's so unbelievably rare that it is very much 'the exception, not the rule' and SE should certainly not be designing around it. I need to do an EX, I'll unbind my DOT and see if anyone raises it as an issue
edit: nobody raised it as an issue, no nickel for me