Not all energy is equal. If your data center is primarily energized with coal, then yes, that's going to have a big carbon footprint. If most of the energy comes from wind, solar, nuclear, and hydroelectric, then there is little or no carbon footprint.
I agree with your sentiment, but any unnecessary energy use is still wastage and still needs to be generated, leading to pollution, even if the carbon footprint is smaller than when using coal power plants.
You have to do some clever accounting for it to relevant in some circumstances. Some data centers are entirely powered by hydroelectric power, and use of that power does not cause any carbon emissions.
Hydroelectric power still requires the building of dams, turbines and piping, the production of which all produce pollution. Again I agree that it is much smaller than that produced during the lifecycle of a coal plant, but building something like the hoover dam is not pollution free. Additional use of resources due to inefficiencies is always going to result in more pollution unless we can eliminate pollution from many industrial processes.
Are those hydroelectric power plants connected to a power grid, among other carbon-emitting power plants?
In this case, every kWh spared by your data center still is a potential reduction of carbon emissions : let your hydroelectric power plants run at full power so they still provide this kWh, thus it doesn't have to be produced by the carbon-emitting power plants. Leading to reduced carbon emissions.
Yes, the Internet is relatively easy to decarbonize compared to e.g. air travel.
But still, the energy consumed might be used for something more useful instead. Or binge watching Netflix replaces an even more energy intensive activity. Who knows.
