But modern displays add unnecessary latency on top of that. HDTV CRTs often did too. Input devices sometimes add latency too. It's really not too awful as long as it's consistent, real musical instruments have latency too (especially pipe organs! but organists manage to figure it out). It's not as much fun if you need to hit the note when it's visibly far from the 'goal' section, or if the judging becomes visible a long time after the note --- shortening the feedback loop is good.
More-modern displays (obviously including LCD and OLED, but also CRT displays that themselves have a framebuffer, as was also a thing) always add additional latency.
0: It's not like we can just somehow convert an existing closed-source thing like Rock Band 3 into a 240Hz source.
The company that made Rock Band, Harmonix Music Systems, has amazing beatmatching technology that has been used in countless games and is even available in the newest versions of Unreal Engine, thanks to being currently owned by Epic Games. They've been developing this technology since the mid 90s.
The main difference between CRTs and other display types, is that the other display types are all largely sample-and-hold - they display the whole frame line by line, hold it for an amount of time, then begin the process again. They generally lack the decay that happens with a CRT, where the image fades by the time the next frame is to be drawn. Some displays can do black frame insertion, but this is a poor substitute. It requires double the frame rate of the intended output, and it reduces effective brightness. I'd like to see an OLED display that could simulate the phosphor decay on a per-pixel basis, to better simulate the scanning process of a CRT.
Would it really be 0 though? Assuming 60Hz, the bottom of each frame is scanned out 16ms after the top. Assuming that Rock Band 3 renders an entire frame before displaying it (definitely true) and that it actually renders at 60FPS as opposed to rendering at a higher resolution and tearing (definitely true on console, might not be true on an emulator?), the video latency will range from 0ms for the top of the frame to 16ms for the bottom, for an average of 8ms.
Admittedly, I don't know what Rock Band 3 calibration numbers actually measure, e.g. whether they already take into account factors like this.
If you can manage to render at a high frame rate then you could reduce latency by tearing, but at that point, I feel like you're leaving a lot on the table by not using a 240Hz OLED or something, which can show the entirety of every frame.
Supposedly OLED has comparable response times to CRT anyway. The article says that OLED gaming monitors are unattainable, but it's 5 years old and things have changed.