The part that takes a long time (i.e. the "bioinformatics bottleneck" I referred to), is that once the sequencing data is stitched together, you end up with a ton of variants, and you don't know which (if any) are clinically significant.
Imagine that each nucleotide in your genome is a marble, and that the entirety of your sequenced genome is a 1-story building filled with marbles (that's how many nucleotides are in your genome), and that each one is supposed to be a specific color out of 4 possible colors. Now imagine that 10,000 (or more) of those marbles are the wrong color.
Primary analysis (putting your sample into a machine and essentially getting back a list of what color all your marbles are), as well as secondary analysis (i.e. the process of sorting your marbles into the correct order so that you can actually tell _which_ marbles specifically are the wrong color) together are what cost less than $1000 and take less than a day.
The real problem is that you may find that 10,000 (or more) of your marbles are the "wrong" color, but 9,900 of them make absolutely no difference in a clinical sense. To be clear, a marble that's the wrong color is a "mutation", or "variant". Maybe this mutation makes my eyes slightly bluer, or my finger nails a little harder.
In other words, the part that takes a long time is actually going through each mutation and figuring out which one (out of the 10,000 variants) is clinically significant or relevant to the disease/symptoms you seem to have, and then figuring out if there's a known treatment for that particular root cause. Currently, this is done by employing MD PhDs to look through each patient's sequenced data, and then cross-referencing that with the millions of published studies to see what has ever been seen before, or is known to be associated with some disease.
And it can take a human hours to a day to do this per patient. So, the number of patients times the amount of time it takes per patient, divided by the number of MD PhDs a lab can hire to do this, is what leads to the backlog.
So, actually yes, it is computational power... but it's human computational power.