I think that's not the best analogy. You're imagining a constant amount of mutations (artillery shells) spreading over the size of the genome (the beach). It doesn't quite work like that, which is why mutation rates are usually measured in errors per base pair per generation.
In fact, copying DNA is more like downloading a large file over an unreliable network. There's a certain chance that each individual bit is flipped and the file becomes useless. You can reduce that chance by sending it multiple times, or introducing checksums, both of which add redundant data. But simply adding an extra TB of junk bytes to your download won't help preserve the integrity of the original file.
In fact, copying DNA is more like downloading a large file over an unreliable network. There's a certain chance that each individual bit is flipped and the file becomes useless. You can reduce that chance by sending it multiple times, or introducing checksums, both of which add redundant data. But simply adding an extra TB of junk bytes to your download won't help preserve the integrity of the original file.