Current Soraka doesn't function as you described.
Current Soraka forces you to focus her while she builds tank and can pump out more HPS than most champions do in damage if you don't focus her.
Soraka should be one of the squishiest champions in the game, but is actually deceptively durable with above average starting armor and health compared to Janna/Nami/Sona.
I compare to those three since she shares the same Mana Regen base/growth and plays a very similar role of heal/peel instead of Bard/Morganna/Karma who can be much more aggressive naturally.
---------------- Armor Level 1 ------ Health Level 1 ------ Armor 18 ------- Health 18
Janna ----------- 19.4 ------------------------ 487 ------------------------ 84 ----------------- 1813
Nami ----------- 19.7 ----------------- ----- 489 ------------------------ 87.7 ----------------- 1747
Sona ----------- 20.6 ------------------ ----- 482 ------------------------ 76.6 ----------------- 1791
Soraka --------- 23.4 --------------------- ----- 529 ---------------------- 88 ------------------ 1825
On every margin Soraka is ahead, in particular her early game stats. The only stat she truly has horrible is her health regeneration (2nd to worst only behind mini Gnar).
Knock her down 3.5 armor and 25 health from her starting stats and she might actually have a riskier laning phase to pay off for her insane team fighting and mid-game. It's possible she is still too strong and needs her base healing values knocked down a bit even after this but this at least puts her WHERE SHE SHOULD BE as a defensive support.
On Grievous wounds, this is pre-season, lots of experimentation is happening, if the current iteration of Grievous wounds is too weak (only affected self-heals) and the cause of this, then Grievous wounds was just a bad band aid anyways.