The problem with the analogy to the phone system is that conversations via phone are transient and private. There is no place with the AT&T logo on it where you can go and see that awful thing that person said. The internet itself is a much better fit for the phone company analogy, and indeed internet service and backbone providers have pretty much entirely been able to stay out of this.

A better (though still imperfect) analogy really is media: TV stations, newspapers, magazines, radio stations. And indeed you see similar problems there as the online media companies are facing now. The biggest difference is that traditional media companies were forced to make editorial choices because of physical constraints - physical space for print, airtime and spectrum for TV and radio - so this question of whether you could just let anyone say anything in your publication or on your broadcast just never really came up.