Could you explain why that is the case? It seems unintuitive.
The artillery that lands on the plain may strike an advancing unit, or it may fall (possibly harmlessly) between a set of advancing units. The artillery that lands on the narrow beachhead is more likely to hit a unit.
This analogy is far from perfect: sometimes mutations are good, which is one primary driver of evolution. Non-coding regions and/or "baggage to be refactored" (paraphrased great-great-gp comment) in DNA (the regions of the plain/beach not occupied by an advancing unit) can absorb "errors". Also, there are other types of mutations (insertions, deletions, ...), aside from the single point mutations that this analogy was attempting to help convey.
The point is: it's like bunching up a lot of important things over a few points of failure. If you increase "the genetic surface area", you lower the chance of the important thing getting hit.
On evolutionary scales, viable DNA has been selected with a lot of non-coding (and sometimes useful) regions, we know that if we reduce that down, we are more likely to be susceptible to fatal mutations on coding regions (e.g. a region that codes for a vital protein).
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.
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.
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.