However, if genetic mutation count is time-dependent but totally independent of the size of the genome, then having a larger genome actually does protect you from individual mutations, and it would do so exactly using the mechanisms described previously.
Think of two genomes, one large and one small, both existing throughout time. Both will accumulate a similar quantity of mutations from mutagenic processes which are time-dependent like radiation exposure.
Basically, trying to give an example of the grandparent's point. (i.e. fewer nucleotides to be flipped -> more likely that an important one will be). I agree that it was a poorly executed analogy. The metaphor I was trying to make is that on the 'vast field' a random single point mutation is probably going to land on an individually unimportant nucleotide, and in the 'narrow beach' (the smaller strand/higher geninfo density) an individually important nucleotide is more likely to be hit. I'm still probably not articulating my point well, sorry.
But I think your analogy is better for a subtly different point; describing how DNA replication works in a system, where stands can be selected out, errors corrected, and genetic information can be preserved at a systemic level.
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.