Michael, I have very little experience with what, arguably, could be called next-gen karyotyping, or "optical genome mapping" (OGM). It's another area of genetics technology that has experienced massive leaps in just a few years.
Very briefly, because this probably won't be on many genealogists' radars, karyotyping is basically a structural analysis of the chromosomes, technically one of a few types of cytogenetic methods. It traditionally looks for defects or abnormalities on, loosely speaking, kind of the civil engineering front rather than the chemical side of genetics.
Structural chromosomal variations can result on a (relatively speaking) large scale like the existence of an extra Y chromosome or trisomy 21, or at smaller scales like chromosomal deletions, duplications, translocations, or inversions. Those "smaller" variations--again, traditionally--have been detectable when on the order of at least a few million base pairs.
I haven't researched it, but it's possible that Bionano and others are stepping into a new direction with a hybridization of array technologies combined with OGM. This ties into the longwinded post about what in the purported complete genome sequencing was still left out of the reference genome...because karyotyping (hybrid or not) is still structural in nature.
The core reason those highly repetitive, seemingly cluttered areas of the chromosomes weren't really accessible to us in WGS was the mechanism by which the typical lab methods operated. It conjures maybe the wrong impression, but the standard was/is "shotgun sequencing." The chromosomes would be broken up into tiny segments only a few hundred base pairs long. One pass, or read, would return data for (theoretically) all the nucleic acid values. Then it was done all over again; ergo the term "coverage" as in 15X, 30X, 60X: the number of passes performed. So what you ended up with was one extraordinarily complex jigsaw puzzle. The computational power came in after the fact to try to take all that data from those roughly 10 million segments of chromosomes sequenced at each pass and then reassemble it so that all the (hopefully) overlapping values from each of the, say, 30 passes could be reconciled and each base pair could be put in its proper place and order.
A lot of us are familiar with short tandem repeats (STRs) as the basic tests for the Y chromosome, and autosomal STRs are what's used in standard forensics. These are structural differences, not chemical ones. For example, DYS448 is defined by--clustered in exactly this sequence--the DNA letters AGAGAT. The nucleic acids don't change, but the number of times that same sequence is repeated on the chromosome can differ quite a bit; repetitions up to 20 times, in fact, for DYS448. So we would say that an instance of DYS448 has a value of 12 if the sequence repeats 12 times.
The SNPs (single nucleotide polymorphisms) of our autosomal tests are, by comparison, chemical in nature. They aren't about repetition, but about a single nucleic acid at a single, precise location on a chromosome mutating from, for example, an A to a G or a C to a T.
Okay. So. Everybody still with me? 
The vast majority of that 7%-8% of the genome that the Telomere-to-Telomere Consortium says they've successfully sequenced hasn't been inaccessible to us. It's been there all along; we've known it was there; we could get allele values from it.
But... We couldn't accurately put the 10 million jigsaw puzzle pieces together in order to understand it or effectively map it. That's because of the tremendous amount of repetition in those heterochromatic, or palindromic, or centromeric regions.
Imagine for example that a sequence is AGAGAGAG and that it repeats itself 150 times, for a total of 1,200 sequential nucleic acids. And we have chunks of DNA to analyze that are 300 nucleic acids long. You see the problem. How can you possibly know which tiny chunk of the chromosome in your 30 randomly overlapping passes comes first, second, and third?
That's an extreme oversimplification, but that's been pretty much the dilemma.
The state-of-the-lab for STR testing has been variations on classical Sanger sequencing. A reason some have trouble with consumer cost difference between an autosomal microarray test and a Y chromosome STR test. The latter involves more manual human interaction and judgment. Fluoroscopy is used to view the structure of the repetitions, which will appear as banded lines.
I can't comment (despite the word salad above), but I imagine that next-gen optical genome mapping--or hybrids like Bionano's Saphyr System could get to the point where analysis to the level of individual STRs is possible. I don't think it's quite there yet, though.
