Xbox does have native wifi. Usually it stays in low power mode and resumes very fast.

Don't have an answer for the size or power items. Those are legit tradeoffs.

What about Xbox One S? Maybe overkill for your needs, but from a price perspective will slot in between a Roku / FireTV and a PC and performs very well.

Alternately, I'm not tracking the specifics of the Roku audio issue, but what if you picked up a cheap soundbar and just used the TV for video?