These seem like pretty common latency numbers for online gaming. I guess it feels worse when there isn't the movement prediction and other techniques to make the latency feel better since the game isn't running locally.

Those latency numbers are just for the connection to a test endpoint optimized for low/zero latency.

My "ping" on games like Battlefield are in the 150+ms range and I frequently get high latency dropped from matches.

When I had Cable my latency was around 15ms and my ping times were 90-120ms in Battlefield.

Well the issue is that you have input lag on your controller inputs. When I move my crosshair it takes a long to actually show the crosshair moving on screen.

In normal online gaming you do not have that issue. When I move my crosshair in cs:go it moves instantly.

Right, yeah that's kind of what I was trying to suggest. Honestly, I don't really see how this can work in the general case all that well given exactly what you are saying. I have seen some examples of fighting games being played over stadia, but many fighting games rely on frame-perfect input (and purists in communities like melee dont even use certain monitors due to this...)