I’m not sure there was ever a time when they didn’t have taps, but this is definitely not true.

https://en.wikipedia.org/wiki/Room_641A

Even in the days of telegrams, FDR was opening and reading millions of American’s telegrams to use the information therein to target his political enemies.

You can’t build centralized systems that enable spying and not expect people to do the “forbidden” thing. We have to build systems that make this impractical.