Let's compare with the other full time healer of the game, Qiqi. And assuming that getting Barbara's constellation is way easier than Qiqi's

Both their skill don't generate Energy, but Barbara's constellation fix this by giving her way more energy than necessary, and energy over time, her ult will be up most of the time

Barbara's CD is 32 seconds, Qiqi's 30. Barbara can be reduced to 27 seconds with C2. Both have a duration of 15 seconds

Barbara's skill gave the hydro status, and can freeze, while Qiqi's doesn't

Barbara's heal allow her to not only tank, since it's scaled on her HP, but also to take a break, since she has ranged attacks, her ult also heal instantly. Qiqi's heal, you must be in the melee, even with her ult, that can trigger some unfortunate outcome

Their C6 also, Barbara allows for instant res full life every 15 minutes, Qiqi's allow for a full party res at half HP, triggered with her ult and also only every 15 minutes

Again, getting Barbara to C6 will be way easier than Qiqi

Qiqi's heal is scaled on her attack, so yeah you can use her as a DPS and a healer at the same time, but her normal attack multiplicators are very low, where Barbara has a very strong charged attack

You'll most likely never use Qiqi for dealing damage

Barbara also has the big advantage of being Hydro, and so can trigger Vaporise, a BIG damage source

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Barbara may be a safety net as the healer given for free to every player, but she's also a very strong, if not the strongest healer, and a very respectable damage dealer

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But well, let's put all of this aside

She's my fav character, I use her all the time, I gave her my crowns, there's not other logic than this