ive played most of the healing specs, and i feel like most of them dont have enough room on their bars to fit damage spells.
like your main job is healing so you want your healing spells and cooldowns to be easily accessable. i main holy priest and i have so many spells between regular healing spells, holy words, cooldowns, trinkets, dispels, and whatever else. i can fit the damage spells on my disc bar because they have a few less spells then holy.
my alt is a resto shaman and they have like just as many spells if not more then holy priest. i dont have any room or keybinds to fit in 4 dps spells (flame shock, lava burst, lightning bolt, and chain lightning).
my other alt is a resto druid, but its actually really easy to do it when you go feral affinity. your cat form bar is separate from your non cat form bar so you can have exclusive bars for each.
i havent played holy pally or healing monk so i dont know how many skills they have
i think theres a big inequality between the sharing of kits for these hybrid classes. when you play ele or enhancement shaman, you only have to dedicate 1 slot for healing surge in order to heal. but when you play resto, they expect you to dedicate 4 slots in order to do damage. on top of that, dps bars usually require less skills. like most dps rotations use around 5 buttons, so you have plenty of empty space. but most healing kits use more then 5 buttons - maybe like 7-10. so not only do healing kits inherently have more buttons, they also require more buttons for damage spells compared to the other way around. its just too much. maybe they should simplify the damage spells on healers so its only 1 button. like just lightning bolt or just wrath instead of having them manage dots and procs and stuff in order to damage
another route would be to have their damage spells do something in regards to healing. i really love playing disc because this is the case. smite will debuff enemies so they deal less damage with their next attack. and all of your damage gets converted to healing at somem percentage. if other classes had mechanics like that on their damage abilities, it would be way more appealing and common to use them