Why is the trace impedance of a single-ended trace on a PCB fixed to 50 ohms or 75 ohms (for video signals)? Why can't it be fixed to any other impedance values?
Short answer: In transmission line theory, the lowest loss is at ~75 Ohms. The highest power handling is at ~30 Ohms. 50 Ohms is just a tradeoff between the two. You can make the impedance whatever you want, as long as they match (but sticking to 50/75 is most common).
Higher impedances are used many times in audio applications or measurement equipment, for example. The 50/75 Ohm systems are usually for signal transmission of some sort (A/V, radar,communications, etc.)