As human beings, our minds are wired to categorize everything in the world around us. It's a natural and important aspect of being able to make sense of the seemingly infinite data points we encounter each day. However, categorization is not always a perfect science, and this is especially true in the world of modern music.
Alternative rock was a concept born out of the 1980's, and was an umbrella term that the record industry developed to describe a group of bands and artists who were making music outside of the norm of mainstream rock-n-roll. Mainstream rock at the time was dudes with long hair playing music that was rooted in the likes of Led Zeppelin, Black Sabbath and others (crunchy overdriven guitars, wailing voices, in-your-face guitar licks etc). A band like The Cure comes along, with some punk influences, and suddenly it represents an "alternative" form of rock, or so the theory goes.
Thus the industry takes the term alternative and runs with it. The label is later applied to the Seattle grunge movement (and all the derivative music that flowed from that, or is associated with it), so you now have a tag stuck to bands like Nirvana and Pearl Jam, in addition to the likes of The Cure, REM etc. Even Creed and Nickelback (gasp!) are linked to this alleged genre, as well as numerous other bands that have little to do with one another aesthetically.
The plain truth is that there is no alternative genre musically speaking. At least not in the way that heavy metal is a genre, or EDM, or jazz, blues etc. There is no common musical language or values shared amongst all bands that carry the alternative label. It's become a completely meaningless term, yet the industry persists with it.
What's more, so called alternative is now the mainstream. Metal and hard rock, while still having a niche audience and new music being made, is mostly dead from a commercial point of view. The Sirius satellite radio channel Alt Nation, which I listen to from time to time, represents an "alternative" to nothing. It represents the mainstream. I cringe when their promos say things like "All the alt-rock you can handle" or some such (I'm paraphrasing, but it's irksome...the mere name of their channel irks me).
Do I have a better term? Probably not. Modern rock? Contemporary rock? Pop rock? I don't know. It's not my place to decide that, but I do feel strongly that alternative rock is a term that has run its course and needs to be discarded.