I think you are not sufficiently recognising how much structural variation can be resolved from short reads. There is certainly some that can't but a large proportion can be with the right tools.
I've participated in several large projects that worked to detect SVs from short reads in humans. The results, which remain best of class, are simply disappointing. A tiny fraction of the variants detected were actually resolvable to near-base pair resolution. The vast majority were described in approximate terms, using estimates of breakpoints and allelic structure.
Most structural variation I've seen based on whole genome assemblies is not even classifiable into neat categories like "deletion" or "insertion". If you think that "most" things are detected with short reads then you are deluded by the dominant technology.
"No human genome has ever been completely sequenced" https://news.ycombinator.com/item?id=15534325 There are a lot of gaps where the amount of repetition makes it impossible to reassemble a complete picture from tiny fragments.
Most structural variation I've seen based on whole genome assemblies is not even classifiable into neat categories like "deletion" or "insertion". If you think that "most" things are detected with short reads then you are deluded by the dominant technology.