True, although it would probably not be so bad for the textual content. CPU load for indexing would be relatively low, and the average phone is dumping tons of data over the network to Google, Apple, and whomever else for these same end-result “benefits” already.
But, regardless, ideally, -ou don’t do it on your phone. You pay $10/m for a VPS that does it, and delivers it to your phone via push notification + fetch – same way it’s done now, but without the middle man.
It’s not a solution available to the average Joanne, although it’d be easy enough to achieve. The problem is that there’s no incentive for anyone to make these appliances: most people don’t understand what they’re sacrificing, or don’t care. And while it’s a relatively small amount of work, it’s a large effort for a few OSS devs to take on, and it’d require at least some support infrastructure, apps, and so on to be truly turn-key for The Public. And so, instead, we have TikTok.