> I wonder whether there would be purpose-built hardware that could do the same more cheaply – think F(P)GA.

FPGAs are not cost efficient at all for something like this.

MCUs are so cheap that you’d never get to a cheaper solution by building out a team to iterate on custom hardware until it was bug free and ready to scale. You’d basically be reinventing the MCU that can be bought for $0.10, but with tens of millions of dollars of engineering and without economies of scale that the MCU companies have.