It became illegal because competitor operators were a threat to AT&T. The government made a deal with them by giving them legal protection, getting some political control in return. Even after the divestiture, the Baby Bells had preferential treatment and received automatic mobile licenses when the technology appeared.
Secondly, it's kind of silly to think about web monopolies when users can freely change operators. Google, Facebook etc have to work hard to maintain their users.
A natural monopoly doesn't need legal protections, it will continue to exist regardless. The very reason competition was banned was because it was possible.
Once upon a time, Altavista was The Search and MySpace was The Social Network.