PoE was created exactly for this purpose! The converters aren't tiny by any means, but they can get pretty darn small if the device doesn't consume much power. Plus, its routable using existing wiring in a house, uses AC to transmit and avoid resistive losses, and is backwards compatible with existing Ethernet tech. Plus if you need internet connectivity, you only need one wire and you can cut your power consumption by ditching WiFi.
> [PoE] uses AC to transmit and avoid resistive losses
What? PoE (802.3af/at) operates at 48V DC. [0]
There is no AC being transmitted in PoE. 48V DC is used to avoid power loss due to small gauge wires in CAT5/6 cables, so they can provide power to devices up 100m as per the Ethernet specification.