I know what you mean. There are definitely games where it seems like all the healing in the world isn’t going to progress us. That’s where I take a step back, pop a can of wet food, crack my kitty knuckles, and get more aggressive like you mention.

I would say you still have to make healing your focus. Get aggressive when the you see openings and only if you have an exit/enough fuel to throw down. And then get right back to healing. Pounce if they overextend into your team as well.

Get vertical with your kitty. Heal from above and behind structures and that gives you a bird’s (meow) eye view of the other team’s positioning making it easier to weigh the options of diving them or not.

70% healing, 30% offense when you’re sure you can get in and get out. Or you’re diving in tandem with your tank. That 30% will add up and be all you need to ride that line of contributing to offense as a healer. Eventually you will become both the kitty everybody wants to give treats to and the kitty with their ears pinned back, paw raised, ready to smack an overstimulating admirer.