Like most things advertising evolved and since mass appeal is the objective it makes sense that pop songs, which are simple and catchy would fill the role that jingles once played.
Pop songs, however, are relatively expensive, and even more so if you have an effective commercial that you want to run a lot.
Without doing any additional searching I can name 2 great, current jingles running here is Los Angeles. Powell Electric's, "...we'll fix it in a flash..." and Empire Carpet, "...call Empire Today..."
So now I think they fill the purpose of lower budget commercials, but they are still a live and they are still a great tool for the right job.