Yes, I did think that a RPi Zero might struggle although I have found them more than adequate on DSLStats service with two different Billion routers remotely monitored, router USB power source and Wi-Fi connection is very handy, certainly a much less demanding application of course.
I had my RPi 3B+ in mind which is currently free, I don't use a media server as yet, might be an interesting project and certainly doesn't cost a fortune for the DVB TV m.HAT board.