From the electrical engineering perspective, the earliest relay and vacuum tube computers were built out of elements developed for radio and telephone exchanges.
Indeed. A "main frame" was originally the housing used for the relay switches in the original telephone exchanges.
I've done a ton of research on this, and "main frame" in the computer sense originated with the IBM 701, which was built from various frames such as the power frame, the storage frame, and the main frame (which performed computation). There is a direct (but complicated) path from this to the modern meaning of "mainframe". The "main distribution frame" in a telephone exchange was unrelated.
From the electrical engineering perspective, the earliest relay and vacuum tube computers were built out of elements developed for radio and telephone exchanges. Bell Labs developed the transistor with their phone system primarily in mind. Same with high speed digital data circuits. (Digital audio was demo'd in the late 1940s, deployed in the phone network in the late 50s).
It's not just the physical circuits; much of the theory, too. Claude Shannon was trying to optimize subnets of switches in the phone network, when he proved that binary switching logic is equivalent to Boolean algebra and so such systems could be described, manipulated, and optimized symbolically.
Similarly, both frequency and time division multiplexing date to the late 1800s with telegraphy. One of the first uses of vacuum tubes as switching elements was for multiplexing telegraph lines c. 1940 or so. (The terminology from that era is quite charming - modern Wi-Fi might be described as supersonic harmonic multiplexed radiotelegraphy.)