It probably has to do with when and where the signal was installed, as well. Traffic patterns and all that. For example, most of the major streets in my town have the signals mounted on metal poles. They’re sturdier, and more attractive in the downtown area.
The westernmost thoroughfare at the edge of town, (called, not surprisingly, Western Avenue) though, for years had just the single signals hanging from a wire across the middle of the intersection. Several intersections just had simple flashing red or yellow lights hung from wires. When those lights were installed, that area was heavily covered with orchards that came right up to the street corners in many places. Orchardists probably didn’t like the idea of the city/county installing bigass metal light poles in their orchards, likely requiring removing trees, and so the signals were simply strung between the existing power poles. Also, because most of the traffic on Western Avenue was just agricultural vehicles and the cars of the few people who lived up there, there was little justification for the expense of fancier traffic signal setups.
As the city grew and traffic became congested downtown, the city decided that it would be good to try to route some of that traffic onto little-traveled Western Avenue. By this time, most of those old orchards had been sold and torn out to build houses. Realizing that those simple old traffic signals would be inadequate, they were replaced with the complex signals mounted on metal poles, as part of the same project that widened Western Avenue.
As to why a city would still have the old-fashioned lights-on-a-wire in busy downtown areas, it makes sense that traffic patterns in that city are such that shutting down an intersection to install new light poles is simply infeasible. So they make do with what they’ve got. Installing those big poles frequently involves completely replacing the sidewalks around the intersection, as the old sidewalk doesn’t provide an adequate foundation for those big poles. This can cause accessibility problems for businesses located on those corners, and they complain …