Computers are in the cloud -- so, nowhere and cost nothing. The AI-assisted search result is on a web page and only costs a little bit of screen space. Amazon may have eaten retail, but at least it ships stuff to my door, has a great selection, and employs people.
Data centers are big, noisy water guzzlers that don't do anything and don't employ enough people to matter. They don't answer questions. They don't write code for me. They don't recover my data if I lose it. If I want to take some computer-mediated action, I go to https://... not data-center://... so why do I need the damn thing uglying up my community?
To be clear, I am not saying that these are stupid or naive opinions or arguments. I'm just trying to point out the visibility aspect. There are cogent arguments why allowing a data center would be a net negative to a community even after you factor in the actual benefits it provides (which are often enjoyed by Other People Who Don't Live Here).
It is natural for us to want eg utility-style AI on tap and also not want the planet destruction that data centers bring. (Nor the brain destruction that AI brings.)