Why would this be an exponential process? The error is per base pair per unit time. If a DNA fragment is split cleanly in half, each half should have double the expected time to failure as the whole, because there is half the number of base pairs each with the same likelihood of error as before.

It's just like nuclear atomic decay. For each base pair, there is a small chance of decay each small time step. The chance of any given base pair remaining undecayed through some time T is the product of all those probabilities, which fall exponentially in T. The expected number of total surviving base pair is also exponentially falling.

People are talking about two different things in this thread, and that's why people are talking past each other. Some people think halving means "half the number of base pairs remain" which would be an exponential process, yes. The other group thinks that "halving" means literally cut in half -- a failed base pair cuts the DNA strand into two pieces. That would be a linear decay process. As someone with no understanding of the underlying decay processes it's not obvious to me which one is right.

Yes, but you need fragments of only about 50 basepairs to assemble a genome (or a big part of it) back. A typical DNA strand has on the order of hundreds of millions of basepairs.

The point is that an entire genome (not just 50bp segments) is destroyed in 1 million years.