Insertions and deletions are usually harder to spot with the short reads that make up the data that you'll get back from your typical "sub-1000 dollar whole genome". The reason is simple. There are vastly more possible insertions and deletions that SNPs, and these all must be considered by algorithms in order to detect them. Worse, as the length of the insertion or deletion increases to a reasonable fraction of the length of your reads, it becomes impossible to hope to resolve the event without considering an untenable space of possible indels and opening yourself to spurious matching.
Those cheap genomes have a serious blind spot--- they don't easily yield information about the large scale variation in structure (indels, copy number, inversions, translocations) that are apparently very important to evolution. I believe the field has blinded itself to the importance of large variation simply because it is hard to observe. Recent papers based on long read data have started to respond to this assumption in a serious way (https://www.biorxiv.org/content/early/2016/09/24/076562).
> Yes there are minute aspects which lack perfect resolution
In the context of humans there is ample evidence that the things we are missing with short reads are not minute, but are rather an enormous elephant in the room, see https://biosci-batzerlab.biology.lsu.edu/Publications/Sudman... and http://science.sciencemag.org/content/349/6253/aab3761. They report that some genomic regions are expanding by up to 50-fold between individuals. Some whole human populations feature quarter-megabase duplications not present in other groups. The scope of the studies are actually very narrow, with hundreds of individuals being considered. I would be surprised if this is anything less than the tip of the iceberg, and incredibly surprised if this turns out to be a minute detail.