I also remember hearing neighbors' phone calls and baby monitors on the first cordless phone my family had.
In addition to the privacy issue, I think we've collectively forgotten just how bad those first few generations of cordless phones were. There was limited range (how about those telescoping antennas?), the sound quality was terrible, the batteries didn't last more than 30-60 mins, etc. In my experience, they weren't worth the trouble or cost until around 1998.