So while we do have Nami, we don't have a Siren

Cass doesn't count. That's just a skin. We lack someone like Naga, and Riot could use this opportunity to bring in a champion who is related to Nami or at least of the name race of ocean dwellers. She has about as much lore as Lulu does, and Lulu has infinitely more fanon because of LuluxVeigar. Nami has little to nothing except the "insert: lul reverse nami joke".

Like Naga, I think this champion should be a hard carry but unlike Naga, he/she ("she" would be more recognizable but "he" would completely break the trope if done well) should have a baiting playstyle similar to the Sirens of Greek mythology as opposed to just having song in their kit, but also be focused on spells and not autos.

There's also a strategic niche that's not been really explored like...ever. AP mages seem to be all about just raw damage and buying utility to stay alive. On the opposite end of the spectrum, you have someone like Elise that has shitty AP ratios but high base damages, so you can build her tanky cdr and do a lot of damage over the course of a teamfight.

Why not take both to the extreme and place them into one kit? Neither would be useless in the other build, but they would be substantially less effective. The well-defined niches would be focused on seiging/poke and high, short range dps. Their passive and ult would accentuate this dichotomy and their third basic ability would cover up one weakness so that the champion isn't too easy to mess up. An example kit:

Passive: If Siren has vision of 3 or more enemy champions, a geyser spawns over two seconds at Siren's current location (Radius 150). While standing on this geyser, Siren restores 10% max health per 5 seconds. Geysers last 5 seconds and cannot be spawn more than once every 60/40/20 seconds.

Q: Siren deals 30/45/60/90/105+0.5/0.6/0.7/0.8/0.9AP magic damage to all enemy targets in a line. Upon colliding with terrain, the projectile ricochets once with the same angle as approach. Targets can be damaged multiple times.

Empowered: Deals 40/50/60% less damage but now ricochets up to 2/3/4 times.

cooldown: 16/15/14/13/12 seconds.

W: Siren causes waves to revolve around him/her, dealing 5/7.5/10/12.5/15+0.05AP magic damage per wave. Waves strike every 0.5 seconds for 2.5 seconds. Cooldown reduction reduces time between strikes by the amount of CDR without also increasing the duration to +0.5 seconds per 5% cooldown reduction for a maximum of 6.5 seconds.

Empowered: Decreases time between strikes by 20/25/33% and increases armor and magic resistance by 25/45/65.

cooldown: 13 seconds.

E: Siren begins to sing, dealing 50/80/110/140/170+0.6AP magic damage to all enemies within 800 distance, dealing less damage the further from Siren an enemy is (down to 25/40/55/70/85+0.3AP at the edge). Siren is slowed by 70% for 2 seconds but also slows all enemies within 800 range. Slow increases based on distance to Siren (15-99%). Targets within 250 range are charmed instead. Slow efficacy updates dynamically.

Cooldown: 20/18/16/14/12 seconds

R: Passive - Siren can permanently upgrade Q or E. This can only be done up to three times per game.

Active - Siren summons a geyser at will. If Siren's Q is more empowered than Siren's E, casting Q while on a geyser will increases the number of bounces by 1. If Siren's E is more empowered than Siren's Q, standing on a geyser while E is active heals Siren for 33% of the damage dealt to champions. If Siren's Q is just as empowered as Siren's E, Siren does not gain any additional effects while standing on geysers.

cooldown: 40 seconds

Geysers spawned by Siren's ultimate do not share a cooldown with Geysers spawn by Siren's passive.

The kit rewards good positioning and aim while giving Siren some ability to really outplay his/her opponent. The DR on multibounce Q really hurts players would would just nonchalantly throw Q into the jungle and hope for the best while also hurting poke in mid air to keep it more situational as opposed to Ziggs, Lux, Xerath, Nid Qs being "Is it up? Cast it." The W rewards tanky building but due to Siren's lack of initiation, Siren requires his/her team to initiate first and then followup with E so that W can be cast with impunity.

The passive is there to give a bit of a tankiness for teamfights and objectives while also letting Siren have some agency of their spawning with a relatively short cd ult.

I think this accomplishes at least thematically what I'd like Riot to use for a Siren champion that has a lot of role diversity beyond just a burst APC.