Tymnet and others built nearly trivial hardware and not so trivial software for such minicomputers to perform statistical multiplexing and it worked like a charm. More detail is provided here. By 1969 we were demonstrating the first of our technologies to do this.
The phone company (AT&T) was certainly aware of the growing demand for remote terminals but their plan was for users to pay the phone company for long distance calls using one of the modems built for the phone company by Western Electric. Perhaps that plan colored their view of statistical multiplexing. Besides the phone company was a legally established monopoly over something vaguely called ‘communications’. But their monopoly was waning.
Gradually it became apparent to all that independent organizations could make a real business of leasing long lines from the phone company, distributing minicomputers broadly to multiplex those lines, and avoid long distance tolls. Eventually, in 1976, the phone companies, collaborating thru CCITT established X.25, a standard for such networks. X.25 became somewhat successful but Internet was destined to supplant it. The phone companies, protecting their revenue stream, were too late. The politics of communication monopolies were dying everywhere in the world.