Calibrating a monitor is intended to ensure that colors on your monitor closely match colors on an ideal reference monitor. That's not the same thing as ensuring that two different colors on the same monitor actually show up differently; that's a much looser quality standard, because even a badly mis-calibrated monitor may still show both colors as distinct wrong colors.
I would only expect poor calibration to break this test for colors near the edge of the display's gamut, or if there's a drastic-enough shift that the color space's lack of perceptual uniformity means a numerical difference that should have been visible ends up in a different part of the color space where that same numerical difference is not perceptible.
Well, I initially ran the test on my cheap vivo phone when I switched to my Motorola the difference was very noticeable, there's obvious color crushing/reduced visible color gamut on the vivo, they're like chalk and cheese when compared side by side.
BTW, I used to calibrate color grading equipment for the film processing industry and the controls were strict, 18% gray walls, D65 calibration sources, densitometric equipment, Ishihara tests for me, etc. so I'm well aware of the issues.
I would only expect poor calibration to break this test for colors near the edge of the display's gamut, or if there's a drastic-enough shift that the color space's lack of perceptual uniformity means a numerical difference that should have been visible ends up in a different part of the color space where that same numerical difference is not perceptible.