Round connectors were absolutely used to transfer data, for example audio and video in the form of RCA plugs and many other examples back in the day. Another example is coax cable for TV signals (both analog and digital) and also LAN.

However the lack of distinct interface channels leads to a bottleneck in bandwidth. So as the need for bandwidth increased many of those were replaced with multi pin versions. This is much harder to do with round connectors and there isn’t that much benefit, so they mostly got ditched.

However round connectors still have their place, for example tiny little coax connectors found in many devices to carry signals. Wifi antennas and such are connected this way.