Why would the SCH job quest available at level 30 feel obligated to teach you how to attack when you've already "mastered" the art of arcane magic as of completing the ACN class questline? If anything makes perfect sense that the one job in the game that starts as a DPS and transitions into a healer would canonically need a teacher to help them become accustomed to mending wounds on the battlefield since they're already capable of inflicting them. None of the examples you listed say anything remotely close to "you better not attack your enemies or you're a bad healer." If anything, they're reminding you that since you're on healing duty now, that it's okay to stop, take a moment, and assess the situation as attacking is now your second priority.
You shared video of footage in another post, but I really don't understand how that's supposed to prove your point. You've got some WHM's spamming Cure on full-HP tanks or near full-HP tanks, not relying on Regen all that much which would be far more effective back in the day at keeping the tank healthy and conserving MP for you in the long run, and otherwise are just I guess taking breaks to pick their noses? How is that supposed to represent what the designers intended for their design? If that was all they wanted healers to be capable of, then that's all they would've given healers to do.
There's so much time where no one's getting hurt in those fights, and in all fights in this game. What is the design intention for those big empty spaces? In case the Healer needs to grab a snack? Take a bio break? So that healer is a role you can play while you make yourself dinner, or are taking your dog for a walk? If healers were ever meant to only heal, the game would be designed so that they are required to only heal. Yet that's clearly not the case even in your videos. Just because the healers in that video were nearly catatonic does not mean that's all healers were capable of or that's only what was expected of them from the actual game.
Sure, all footage of early ARR content has healers playing terribly, but the secret is that all of us were bad at the game. It takes a long time for a brand new MMO to have its community develop knowledge and skill. Someone who's started playing tennis 3 months ago is not going to be as good as a tennis player who's been playing for a year. That's normal. And what's more, logic taken into the game was largely taken from other MMOs like early WoW and FFXI where you didn't have fixed parties, scripted encounters, built-in resource management systems... Even in its more crude shape back then, FFXIV was a different beast.
You can fold a cup out of notebook paper and pour coffee into it, but that doesn't instantly make it the apex of how coffee is meant to be drank nor is it a representation of how the coffee roaster expects their drinkers to consume the product. You can play a healer terribly or using logic from a different game, but that doesn't make it the intended way to play.
Yes, actually, the combat does say it. In fact we don't even need to translate it from Sanskrit. It's plastered all over fight design in every corner of this game that it's not even funny, written in magic ink that conforms to your first langauge, gives you a free pen with a green cross that has a smily face and the quote "remember to DPS when you can" and a sticker that reads "I healed. I DPSed. I conquored." There are looney tune style massive neon red arrows pointing to that copious amount of healing downtime with a sign above that lights up and says "DPS now!" and turns off as soon as a raid wide goes off.
EDIT: Also on the topic of "but it's for solo content." Well actually, FFXIV's format would've perfectly enabled healers to have 0 DPS buttons if that was the intent, because of the job change system. If the designers really wanted healers to only heal, all they had to do was kill the idea of Arcanist. Conjurer is a DPS who branches into Black Mage or White Mage and share levels. Thaumaturge would've instead branched into Summoner and Scholar instead of Arcanist. Thaumaturge and Conjurer are hybrid DPS with heals, and lose their DPS when going healer while losing their healing while going DPS. They share levels, so bam. You don't solo as a healer since there's nothing to heal when solo.