That's not quite correct. There's a lot of NIMBY pressure in cities, where land is scarce and there's lots of people to attend planning meetings to block building.
However, if you want to build a datacenter, you don't need to build it in downtown Manhattan. You can build it anywhere, and some places make it easy to build data centers.
By definition local restrictions apply locally. If you want more housing in Manhattan then Manhattan nimbyism really matters. But if you want to build a data center somewhere you have a lot of options. There's no nationwide vote on allowing datacenter construction.
I do wonder if you'll see local community NIMBYs about it though. Electricity prices near data centers go up, right?
While that’s true, and there are several locations that are using their local authority to perform those actions; but, *all* of that is power wielded by elected officials. The smaller the location the less “who voted for this” likely means anything because the decisions that are made that impact all of us are made by a smaller and smaller number of people with less and less authority, but it is still voted for.