The biggest factor in choosing what electric guitar to use on any given song is the way it sounds. And despite all of the mojo involved with strings, solidbody vs semi-hollowbody, etc, a guitar's pickups are still the single biggest factor in determining how it sounds.
The two principal food groups of guitar pickups are humbuckers, and single-coils. Single-coil pickups came first and their lineage predates rock n’ roll by about three decades.
Later (in the 1950s), Gibson's president, Ted McCarty asked Seth Lover to develop a pickup that wouldn't be susceptible to the buzzing that was typical of single-coil pickups. Single-coils are basically magnets with wire wrapped around a series of single poles or one single bar, and they have a tendency to collect all kinds of electromagnetic interference such as bad stage wiring, police radios, lights, etc. McCarty also was looking for what he called a "sweeter" sound than was being produced by Leo Fender's "harsh" single coils.
After trying various designs, Lover came up with humbuckers that were designed to correct this by using two coils wired 180 degrees out of phase. The two coils are placed in the pickup in opposite directions, thus making the pickup in phase and “magically” canceling the hum.
By their very nature, these different pickup configurations produce different sounds. Typically single-coil pickup guitars tones are described as “chiming,” “clear” and “bright.” Conversely, humbuckers are commonly thought of as “thick,” “dark” and “heavy.” In general, humbuckers have a higher output and push the front end of a tube amp harder as well.
We all benefit from a balanced diet and no self respecting guitarist would show up at a recording date with only one electric guitar. The best session players get work in part because they listen to the song, and make careful decisions as to what will sit best in the mix.
Some people suggest that the guitar industry is simply trying to give guitarists GAS (Gear Acquisition Syndrome). Those same people would probably accuse me of being part of their evil plot to take all of your money.
Now, you might think that, but I couldn't possibly say.