Price of power goes up and the local people are not connected to the benefits. You might think they will receive a lot of money in taxes but you would be wrong because they have tax breaks.
Because on-site powerplants owned by datacenter operators are not "just another supplier".
The threat is: This "datacenter power" disincentives buildout of "free" powerplants (by eating up significant demand at very low margins thanks to basically vertical integration); this slows down buildout of "normal" infrastructure (possibly both grid connectivity and power), and the electrical energy market becomes worse for consumers than it is now.
I personally think all of this is very speculative for now, but allowing industry to rely on the grid (which they still would!) while almost exclusively "buying" their own power is a risky proposition from a consumer perspective.
Not to mention the danger of energy production, even nuclear, becoming resource-constrained to the point where datacenter power plants leave no room for municipal plants. We're seeing it happen with consumer hardware; make no mistake on who will get preference.
"Attempt" is doing a lot of work there. Companies are driven by a profit motive, and are practically required to renege on promises that are not legally enforced.
In a different world they would have earned trust and deserve the benefit of the doubt. This is not that world.
You'll notice that I did not advocate against building and grid reconfiguration. Indeed, my company does microgrids. I do, however, believe strongly in being aware of tradeoffs.
In short, I'm very much in favor of building the right solution to a problem.
I am unsure what cognitively triggered an unhealthy response of "this is NIMBYism!" and would welcome a follow up comment to understand your train of thought.