Gregory's Server@skyfaller sure, and you'd be correct in thinking that way.
My perspective is the actual webserver for a plain text website contributes very little to the actual power use when you consider the infrastructure required to route those packets to the device, and the device usage.
Feel free to disregard that analogy and substitute your own appropriate "it technically works but it's not worth it under most circumstances".
@skyfaller interestingly, running a microserver or similar power level device is an application that might make sense for Thermoelectric solar generators - if you don't have space constraints, prioritise environmental impact over cost, and can make one that'll last a decent time, I can even see it being a good option.