Her e-r/ r-e kombo is her most basic ability kombo. It is the only save method she has to trade with most enemy champions. ( High mobility/ranged ones)
Do not consider it her secondary strength.
The ultdamage is just not reliable enough to work with it properly. You may get an ult that is dealing more dmg than usual off, but your e still was necessary to make the tradeoff impactful and in your favor.
Since they lowered the q dmg, and with the unreliability this skill has ( So many rivens/adc flashing my q. If they do that, I most likely die in this fight) anivia is bound to loose more trades by default.
Everyone who played anivia knows how her fighting pre level 6 midlane is. It is realy hard to do anything during this time that has any meaning( using you q always is a risk with a possible gank around) . Now her post level 6 gameplay is going to look similiar. Anivia already was more reacting to enemy actions than anything.
with this change she has to play even more passive, as trades are not going to be in her favor.
And her utility in lane pressure... most champs can clear waves faster with less mana. I do not know any main anivia that played her for that reason. Siege and defending got nerved with and prior to the mage update.
To put this into perspective: Think of lux e dealing only full dmg if it stayed for its whole duration(which is now 1,5 seconds). Dont give her any compensation for this. Half her e dmg if used imediatly. Make it not scale over time or anything.
It is not a good example, but the only thing I could come up with so quickly.