Server side means an excuse to not improve model handling everywhere you can, and increasing global power usage by noticable percentage point, at a time when we're approaching "point of no return" with burning out the only planet we can live on.
The previous commenter is right in that server-side companies have little incentive to do less, especially when they're backed by investors money. Client-side AI will be bound by device capabilities and customer investment in new devices.
Server side means shared resources, shared upgrades and shared costs. The privacy aspect matters, but at what cost?