I've played Janna, Orianna, and Cait since the reworked mana so I can't speak for Nami/Sona/Raka yet (although I will definitely be playing 1-2 of them today). The mana regen helps with Janna's early laning phase (1.8/sec now it used to be about 1.38/sec before) but it only helps with her laning phase before my first back when I would get my chalice. lvl 1 tornado costs Janna 90 mana level 1 shield costs 70, and Zephyr costs 40. You want to max E (her shield) first. It ends up as 110 mana going up by 10 mana each level. Early levels if you got hard engaged on by a Leona, Thresh, Blitz, the enemy jungler, you spent 1/3rd of your mana on your tornado 1/3rd of your mana on your shield, maybe some more on the slow. Aka Leona jumps on your carry Q > E Leo backs off, she has basically full mana, you're almost out of mana. There were some champions (Lulu mid and Janna support specifically) that I didn't rush chalice just because of the mana. I build a pretty teamwide tanky Janna. Locket and Crucibles were always a must and then often Ninja Tabi/Merc Treads, some big armor item (normally frozen heart or thornmail), her Ruby Sightstone, and her Talisman. I will have to test new crucible on her (I feel like the boost in Mana Regen might make it a little helpful) but I have a feeling it won't be as good anymore.
But like I said the difference in mana regen for Janna is has a base of 1.8/sec compared to 1.38/sec, which when it comes down to it isn't going to be the 11-8/sec I almost always had with my Chalice, because even late game it's so hard for Janna to keep her mana in a fight.