I somehow managed to miss the sentence entirely where this is explained (it is used for reading EDID from a connected display). Thanks for the correction!
An on-board battery or capacitor could help to smooth out brief high power tasks, but I don't think it will be able to sustain video decoding & playback at a constant supply of 150mA. I'm really excited for that to be a possibility though, so I hope I'm wrong.
Of course, some TVs might dump a lot more current over the connection, just like what was common with USB 2.0 going well over 500mA.
I've never seen any Chromecast advertising that implies it only gets power over HDMI. All of the media on Google's Chromecast site show either both HDMI/Aux and USB plugged in or nothing plugged in. Pretty much any TV now has a USB port whether it be for media playback or for updating the firmware of the TV on older ones so its not a huge deal to have to plug it.
All of the screenshots I saw before purchasing the original device clearly showed it plugged into a TV with no power cord attached. It looks like they may have fixed it in the newer marketing.