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It's something I've seen in a good number of other games and shows, but so far League hasn't done anything like that. The only two water Champions, Fizz and Nautilus, are all about water's destructive power, which is a bit of a polarized view.
IMO, a support mermaid Champion would be a nice addition.
Passive - Rising Tide: Each time a spell is cast near Yue (including enemy, ally, and her own spells), she gains a charge of Rising Tide. When she has 5 charges, her next spell cast will heal her for 30+(5*level) (+0.2AP) health and the spell's mana cost will be halved.
Q - Vital Wave: (First Cast) Yue begins to stir a magical wave of water, gradually increasing its range, width, damage, and healing. (Second Cast) Yue releases the wave, dealing magic damage to all enemies and healing all allies it passes through. While preparing the wave, Yue cannot attack or use abilities, and her movement speed is slowed by 20%. After 4 seconds, Vital Wave fails but refunds half its mana cost. If Vital Wave strikes a Water Elemental, the Water Elemental receives increased attack speed for 3 seconds.
W - Water Elemental: Yue summons a Water Elemental at a target location, dealing magic damage and slowing enemies around it when summoned for 2 seconds. The Water Elemental is melee, controllable, does magic damage, deals 50% splash damage in a small AOE with its attacks, and deals greater damage based on Yue's AP. Water Elementals last 15 seconds. Yue can only control one Water Elemental at a time.
E - Ocean's Protection: Yue places a shield of water on an ally or herself that absorbs incoming damage for 3 seconds. If the shield breaks to damage, it releases a burst of water, dealing magic damage and knocking back all nearby enemies. If Yue casts Ocean's Protection on a Water Elemental, the burst effect will occur instantly instead of occurring if the shield breaks to damage and will have a larger radius.
R - Purification: Yue cleanses an allied Champion with pure rainfall water, removing any crowd controls upon casting (including suppression), and heals the target. For the next few seconds, the target becomes immune to crowd controls.
"WHOA! THAT ULTIMATE IS OP!!!"
Long cooldown, limited range, only affects one target, and taking out Yue herself is pretty easy to do.
If you have any other "OP! HURR DURR!" comments, you'd better have a good argument to back them up.
"That Q makes Karma's look like a joke!"
Consider the downsides: Yue's is weaker unless she charges it, during which time she can't use other spells/abilities, it doesn't work nearly as well as Karma's spells when her target is low on health, and Yue's version has a longer cooldown.
Also, don't compare Champions only on single abilities; Riot says you kinda can't do that.
EDIT: I have also been considering modifying the Q so that it will have a knock-back instead of a heal, partially as a thematic thing and to make it so Yue can't sustain a lane partner and potentially create toxic situations. It is under debate, however.
"How would a mermaid fight on land? Don't they have fish tails for legs?"
You think I'm suggesting a typical fantasy mermaid? Riot would instantly say "that's boring!", so I'd use a model with human legs and fins along the body, more like a Zora from Legend of Zelda. Much different.
"This belongs in Player Concepts, not General Discussion!"