I just opened 4 streams to plus recording the same game and they are definitely "proxied" ("tuner shared") through channels. My mlb-channels-docker isn't even reachable from my local network as it is on a different machine on another network. (had to patch the docker-img btw to pull the logos from a different url - that's why I was asking if there was a repo somewhere to commit to/branch from).
I didn't set up any tuner sharing in any of my clients - and I am not using any transcoding (maybe that's the issue here?)
Yet - regardless if I stream through FireTV, TS4K and VLC channels log says:
2021/06/03 22:09:57.349017 [TNR] Sharing existing connection to M3U-MLB for ch7777 Cincinnati Reds (clients=3, len=0)
I can confirm that the docker contains eats up ~30% of my CPU every few seconds, but overall my server load (where the mlb-docker runs) is low. ~ .15-.2 - and it's a small VM with only one core that doesn't do much else.
Load on my pi, the channels server in the lan - serving those streams, plus recording another show, plus running a commercial detection is pretty high though - ~3 
PS: I also ran netstat and didn't see any new connections opened on my mlb-server - I might have missed s.th. though - gotta run