Nothing unexpected gete, obviously dedicated streaming device with way weaker processor and less hardware will consumer less power. Though you might be going into other extreme to where quality of stream and all features won't be on pair due to device being way weaker in terms of hardware. While it would be nice if consoles could enter low power mode for streaming, those big chips still will consume way more power compared to low power chip in dedicated device with only small fraction of processing power. But I guess they could "park" or in other words turn off most of the cores and also do similar with graphic card ti conserve more power. Some things like SSD controller probably couldn't be powered off. Also this could hurt snappiness, which us the thimg current generation is about. Plus you can imagine consoles as more of PC like in terms of power consumption, like PC streaming also won't consume that small amount, like only graphic card abd CPU can easily add to 60W+ idle on desktop, even with all power saving features enabled.
But if you really want to minimize power and are ok with some features missing and other compromises, there is nothing wrong with having Chromecast device or something else. In the end that is built to be low power consumption device while on console, main purpose is gaming, streaming is more of secondary function and they don't want to compromise former to make latter use less energy. Though at this point, I would question if it isn't better to have just TV that supports streaming, so you aren't powering two devices, even if in case of Chromecast it is peanuts worth or power.