Otherwise monitors, cables and video cards would have compatibility issues.

You're right, and this was absolutely a thing. Video cards could produce whatever they were capable of, and monitors could display whatever they were also capable of. You could also push resolutions and refresh rates to monitors that was beyond the monitors' specs, and you would also risk damaging the monitor by doing this.

I don't think you were pushing 4000x3000 resolution through VGA.

You don't need to believe me. That's your choice. I had friends that could do the same. This was with a Matrox card and a 21" Acer CRT. The display was nearly impossible to read, and the color mask broke up the individual pixels too much, anyway.

Just like today no one is pushing video streams to giant building sized screens over consumer HDMI or DVI.

Digital video has upper limits in its specs. This is the whole point of this conversation.

Another example is XLR VS 3.5mm jack. In theory you can push audio signal of any quality over both, but XLR by spec is balanced and shielded, while 3.5mm is not. This means that XLR is capable of pushing much better audio.

A bit of incorrect information here. There is no "unshielded 3.5mm spec." Good cables have shields, but not all. XLR doesn't have the ability to transport higher frequencies because it's balanced, or "much better audio." On paper, unbalanced audio is better for short runs because there is more opportunity for XLR signals to have extremely minute signal quality issues due to the hot and cold signal mirroring, but it's so small that it doesn't matter.