The history of computing is usually described as a nice progression from vacuum tubes to transistors and then ICs. But parametrons are only one of the many forgotten technologies that popped up along the way. Magnetic core logic such as transfluxors was used in several computers. Superconducting cryotrons were going to revolutionize computers. Tunnel-diode logic was also briefly the wave of the future. Other significant technologies were microwave logic circuits and electroluminescent logic circuits. I have to say that the 1950s came up with the best names; modern technologies just don't measure up to transfluxors, parametrons, and cryotrons.
See Digital Computer Design Fundamentals, 1962, chapter 6.
Don't forget good old relays.
Right. So many things were tried in the 1950s. There was a lot of interest in nonlinear magnetic devices. UNIVAC had magnetic amplifiers in their "Solid State" computer (1958).
Magnetic devices have the nice property that there's no wear-out mechanism. They're just coils and magnetic materials. They just keep going, for many decades. The Bell System loved nonlinear magnetic devices. There were lots of them, usually potted inside little grey boxes. Here's one of many on eBay.[1]
[1] https://www.ebay.com/itm/318704409860