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The 45° routing makes it easier to route multiple parallel traces across the PCB - I would say that's the main reason why they are so popular. Whereas 90° turns of multiple parallel traces next to each other is a big no-no, since that may lead to crosstalk. And routing multiple parallel traces as arcs will perhaps take up a lot of extra board space needlessly.

Regarding arc traces, they have their place, namely when designing a RF path or PCB antenna. These layouts are often sensitive in all manner of ways:

There's various best practices such as placing all series inductors in a RF filter/matching network at 90° angles in relation to each other to avoid coupling. And matching network components should also be placed as close to each other as possible, to avoid parasitic capacitance. And so on - best practice design rules like that will in turn mean that the trace will end up in whatever shape that makes it easiest to draw the shortest possible RF path between components while avoiding sharp turns or vias.