A protocol for reliable notifications over a 1 bit fallible connection

Why would we ever use the obscenely expensive channel? Surely there are ways to solve this with only the single-bit channel?

Some error correction codes, some cryptographic hash checksums, and now you have a free trustworthy bidirectional bitstream.

The channel is free. Repeat each bit 1 billion times and reconstruct the messages based on that

In practice you still want to optimize for bandwidth, which you can.