60 hz = 16.67 ms
120 hz = 8.33 ms
144 hz = 6.94 ms
240 hz = 4.17 ms
People can easily tell the difference between 60 hz and 120 hz which is just an 8.33 ms difference. Network lag is on top of all that...and it's a two way street: it takes time for inputs to get to the server, be rendered, encoded, received, decoded, then displayed.
It really needs to be LAN speed or ~1 ms round-trip time. Anymore and you'll be able to tell you're streaming.
Even at LAN speeds using Steam Link, you can tell there's a crapload of compression noise in racing games (Dirt Rally). It's much harder to drive fast on Steam Link than it is in front of the computer because that loss in detail...that's right where you have to look to judge the next turn.
It's just... a terrible idea in general...unless all you play is slow, turn-based games.