In the same way that most public utilities are: train stations, railway lines, airports, garbage dumps, sewage treatment plants, military bases and a hundred other things. The negatives are concentrated to the locality and everyone else reaps the benefits.
I get it if you wish to put a 99% self-sufficiency condition (water/power etc) but everything else reeks of luddism and nimbyism.
All of these create a ton of jobs in the local area and many of them provide massive advantages to the local area (except railway lines if you're not near a station I guess).
A sewage treatment plant may or may not be stinky, but I very much want to live in range of one so that my sewage gets treated. Similarly, living near a railway line means I can ride the train. Living near a landfill means that my trash can be managed at reasonable expense. Living near a military base adds huge potential economic value and nominally keeps me safe. Living near a giant AI inference or training facility? Meh -- I could use its services just as easily if it were 1000 miles away.
chatgpt has 900M weekly active users, so a significant fraction of the world population. Given that the user base probably skews towards rich countries, its proportion among the local population is probably even higher. On the other hand what do you think is the proportion of people who take trains, especially in the US? What about steel plants?
So if I drive to work then it's fair game to be NIMBY when they want to build a light rail station? You might say "but even if you don't use it, it's reducing traffic so you're still benefiting!", but if those kind of arguments are allowed, you can make similar arguments about how AI will make the whole country richer because of increased productivity or whatever.