Remember that the great monopoly to be broken up by anti-trust law was in fact a government-mandated one: AT&T. Without the government banning competition, AT&T would have been very much different in 1974 (the time of the divestiture).
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.