Zen would like to have a word with you on that last sentence. As would the Support role as a whole.
'Healing through only cooldowns would be really bad’. Your words.
Lucio? Zen? And Lifeweaver is the same, but for the opposite reason - He only has healing through Weaponry, but he’s not a Healer. In fact, he only beats Zen, in terms of healing numbers. But none of them are bad Supports by any means, and yet they have no way of healing outside of abilities. One ability, to be precise. Cross-Fade and Orb of Harmony, respectively, and Lifeweaver again only uses Healing Blossom.
Why do they work? Because they’re Utility Supports, or Off-Supports as OW players call them. They are made to be played alongside someone like Ana, or Baptiste, who are Healers, or Main Supports.
And it’s interesting. Because I want to talk about Utility, as a whole. As it’s always been Sombra’s whole thing - She’s a Utility DPS. Back before Role Queue was implemented, she often filled the role of an Off-Support, able to put out high damage numbers, but also provided a ton of offensive utility. Which Lucio, Zen and even Lifeweaver all excel at, though Lifeweaver is defensive in nature, not offensive.
And when we look at the Overwatch website’s definition of a Support, this is what it says:
Support heroes empower their allies by healing, shielding, boosting damage, and disabling foes. As a support, you’re the backbone of your team’s survival.
Sombra already functions as a Saboteur. She is already filling the role of a Support. And bare in mind, it never says that a Support has to do all of these things. Hell, since Symmetra’s rework, there’s not a Support who even provides Shields, but it’s still there. So we could easily have a Support added that provides Shields, or at the very least Overhealth. Which is exactly what Mirrorwatch Sombra did. White Hat also exists as a Major Perk, which gives Sombra the ability to heal already on a 3 second cooldown. It’s not ever going to be a major thing current Sombra or a potential Support Sombra would focus on, but it’s a tool she has in her arsenal, even as a Damage hero.
It was when we started slapping healing on everyone’s weapons that healing started to snowball out of control. Mercy was the only Support who could heal with her weapon, back in the day when the game first came out, being accompanied by Lucio, Symmetra and Zen. Lucio and Zen only healed through abilities, and Symmetra covered defensive utility and area control. Still doing Support things, even if she struggled before her first (and best) rework, but doing so in her own way - Providing Shields and area control.
So having a Support Sombra that was still Sombra as we know her, with White Hat moved to be a Minor Perk, reducing her damage a bit and giving her more team wide utility, both boosting allies whilst still keeping her Saboteur identity, she’s pretty much set to be an incredible powerful Support hero. Funnily enough, I actually made a post about what a potential Sombra Support could look like which you can check out here, if you wish: Sombra Support Rework (JFF)
Now, all that’s to say I’m not saying she should be a fully fledged Support hero. I think it would definitely work for her, if the Devs really hit a wall with balancing her, but I don’t think it’s at all required for her to be reworked again, nor to change roles. But given what the Devs define as a Support, and how Sombra’s historically been played, she’s been filling a Support role since she was added to the game.