I mean she's always had a fairly low play rate, and ban rate. She starts to fall off at plat+ and is a rare site nowadays in the Pro scene. She's been nerfed really quite hard in the past to where people almost thought she was useless, and she was designed for counterplay against burst mages in the first place. Here's a link to her entire patch history: http://lol.gamepedia.com/Anivia_-_The_Cryophoenix#Patch_History
I've just published a board post here: http://boards.na.leagueoflegends.com/en/c/gameplay-balance/jtUIq7Oj-anivia-feedback-from-a-seasoned-anivia-main -- which go over my thoughts on the proposed changes. I'd really appreciate it if you took a look.
In short: I think the changes to her Q/W+E are fair, and I am actually in favor of publishing those changes. However, I 100% think that the changes to her R+E/R/E are completely absurd and unreasonable, these changes essentially increase her burst window by 3 Seconds, which is ridiculous since she's a mid lane champion where she fights against champions with much shorter, and much stronger burst windows to begin with.
A counter proposition to an E/R change on Anivia would be to "Ice Champions when her Glacial Storm/R is at half size, or after 1.5 seconds to do full damage on the E. Essentially increasing her burst window by 1.5 seconds from where it is now, instead of 3. Which is completely fair in my opinion.