What do you mean it's not related to healing? DPS rotations for a healer is related to healer gameplay and healing in general. Since downtime exists, it's related to healing because damage skills is a healer's tool to mitigate incoming damage by speeding up fights. If the boss can't use their next raidwide AoE because you contributed to DPSing and killed them off before they got a chance to let that attack off, it means you reduced the number of Medica/Helios/Succor/Benefic II/Cure II/Adlo/GCD healing spells required, then yes it's intrinsically related to healing. Some bosses do get stronger if you let them live longer - Ex bosses using Akh Morn. Some bosses will hit another tankbuster mechanic. The longer they live, the more stressful and taxing it is on the healers - because not only do you have to take into consideration with more incoming damage and having less MP from using more mana-intensive spells, it's assumed the party will still be able to perform at a certain standard as the fight progresses. As you may have experienced, the longer a fight goes - even in a scripted fight - the easier it is for a player to lose concentration and start taking more avoidable AoEs and the more MP it is required to keep the party running. So yes, it's completely related to healing.
Easy way to see this would be WHM Holy on trash packs - more damage to mobs + stuns = less outgoing damage on the team + less hits the tank will take. The faster something dies, the less time it has to hit.
If you were referring to how AST's card system isn't related to healing, it is completely related because it's related to healer gameplay. The old card system enabled AST to buff / increase def/ party AoE with royal road. It was used in conjunction to your healing skills. More mitigation = less incoming damage = less healing. More damage = faster fights = less overall healing required.
It's exactly due to raiding being very difficult during ARR because of constant party wipes and healer DPS helping to contribute to ensure those runs become successful that the idea of healers DPSing became a thing. It's also why people say a good healer doesn't overheal. Healers would save mana by not overhealing and save a GCD to DPS and speed up the fight. It's also partly why some healers would overDPS and how a healer misjudges the need to heal assuming the party would be fine when they start taking avoidable AoEs. Granted, healer DPS may not be required in most fights - but a good healer will DPS regardless because this is a way to actively mitigate and reduce stress on both the healers and the entire party in general.
As for AST's current system, it has a weaker damage up effect per card that is hard to see without a parser unless you pop both divination and the buffs together, but it still is completely related to healing. It speeds up fights which means less incoming damage. The only difference is the fun involved with the fight. Pressing one button for 12 to 18 minutes straight gets dull fairly fast. This is what healers might have been envisioned on this expansion, but that was not the case for previous expansions. With healer complaint being as high as they are, not changing the current paradigm for the sake of balance will only lead to what AST has now - complaints for a Balanced and a functional job, but being played less as a whole.
If what you say is true about how Savage/Ultimate is the focus of changes for Balance, then healer gameplay & enjoyment starts from there - where healer DPS actually does matter because healer DPS does make the difference between wiping and clearing. If people at Savage and Ultimate complains of a lack of DPS rotation on healers, then it should a valid concern for gameplay enjoyment. I'm all for all healer jobs getting an extra DPS skill if it means breaking the boredom of pressing one button consistently.