For IVF embryos, it's the small amount of genetic material which makes accurate sequencing difficult. For standard human whole genome sequencing (WGS), the fastest times are down to five hours[1] (although that is exceptional), for which the imaging was massively parallelized and it seems that the choke point was computational for that particular case (sequencing like this basically multiples the DNA, shreds all the copies, images each shred in a reasonably-parallel manner, and then uses longest-common-subsequence to put all the shreds back together digitally).

Average WGS times for something a person can buy for a couple hundred dollars take a few weeks, and will usually be bottlenecked by logistics (mailing things, getting it to the lab, etc.) and then the imaging (a flow cell runs the fragments over an imaging device; parallelization is accomplished by running multiple flow cells at once).

I might be slightly off on my terminology here but the idea is broadly correct, I think: Differing grades of sequencing are determined by the average depth of fragments for each base-pair -- e.g. 1x sequencing implies an average coverage of one fragment per base-pair, which could lead to mis-aligned or improperly joined samples. 30x-50x sequencing is pretty common for consumer grade WGS these days, which gives a higher number of fragments that allows you to weed out bad reads or incorrect joins of the sequence, though errors can still occur. This is usually sufficient for diploid (having two values for each base pair, one maternal and one paternal) humans, since it's important to determine if the basepair is heterozygous (different bases from each parent) or homozygous (same base from each parent). However, if you're doing cancer sequencing, a tumor may contain many many more different genes, so a massively deeper sequencing depth is required to ensure you have reasonable statistical certainty on what variations occur within the different genomes. Higher depth == more material == longer time to sequence since you have more material to image.

Note that services like 23andMe are NOT doing whole genome sequencing; they are using specialized flow cells that only examine certain specific sites on the genome called single nucleotide polymorphisms[2], which are traits or indicators that are turned on or off by a single nucleotide, hence it being much cheaper and faster to run.

[1]: https://med.stanford.edu/news/all-news/2022/01/dna-sequencin.... [2]: https://en.wikipedia.org/wiki/Single-nucleotide_polymorphism