Lots of folks have rightly pointed out that the electronics for cellular telephones wasn't ready in 1947 but neither was the switching infrastructure. The first customer-dialed long distance telephone call wasn't placed until 1951 and it took at least the better part of a decade for that technology to be widely available across the US. Telephone switching was largely electromechanical until the early 1970s with the first Electronic Switching System having been deployed in 1965. But even at that time, the #1 ESS didn't have the sophistication or compute power to keep track of phones and perform handoffs as they moved from cell to cell. (The first true cell phone networks were built on the 1A ESS that came over 10 years later.)
Having said that, AT&T did demonstrate the cellular concept with a pay phone service on the Metroliner train service between New York City and Washington DC in the late 1960s. The pay phones used land mobile radio channels and would switch from channel to channel with a reuse pattern up and down the Northeast Corridor. There was a lot of work that had to be done and technology that had to be developed to get to that point - it took them a good 20 years to build this proof of concept, which they did prior to the FCC allocating what ultimately would become cellular spectrum. In fact, the Metroliner payphone system was a key milestone in opening up the conversation to get UHF TV channels 70-83 allocated for cellular.
TFA would have been more accurate if it had focused on 1970s as lost time for cellular development, but I think it was only a marginal effect. Much of the technology was still being developed (like Marty Cooper's handheld cell phone) while the lawyers and lobbyists haggled over the spectrum. By the point, it was pretty clear cellular was going to happen, it was just the regulatory details that had to be worked out.