Years ago Amoco would produce a hundred +/- products from crude ; so I don't understand your question . Aside; my favorite was "Trombone slide oil".

True but he did say as regards to vehicle fuel grades not all distillation products. Whether that's true for crude oil that I wouldn't know.

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Why is crude oil refined into only three grades for vehicles (heptane, octane, and "diesel")?
Actually a lot more components are used. Heptane and octane are just reference points for the "quality", specifically normal-heptane and a specific iso-octane (2,2,4-trimethylpentane). The mixing of fuels can include a lot of component from the crude oil distillation and other sources as well. For example you can mix in iso-nonane (C9)in the summer if the altogether octane number of the "mix" stays right. For the winter you can use butane to the "mix" - it also improves the cold ignition properties. The goal is to produce the most product with good quality.

I'm wondering what the relative prevalence of each hydrocarbon is in the crude we typically process in the U.S., as well as the difficulties of separation and cracking, in order to better understand things like: Why does octane command a retail market premium? And why are heavier distillates all lumped into the diesel market instead of, for example, using H9 to run gasoline engines at higher compression ratios than they can with H7/H8 blends?

I can't tell you specifics about the US (I'm from EU)... but separation is usually achieved with distillation or vacuum dist. It provides products according to - if we simplify - boiling point (and not specific components). This will already be a mix of hydrocarbons. To give a feeling for it: if you say octane or C8 , that is 18 different isomers with different properties, heptane(C7) has 9 different, nonane(C9) has 35(or 36?) different isomers... if the boiling point is near it will go in to that "hydrocarbon soup". Which will go for the final mixing as I wrote above.
Cracking... thats a bit different, also depending what kind of cracking is used... the and is the same: separating the products. And the "fuel product" will go the same way as above.

Octane premium: with high octane number it is a ready product or even can be "thinned" down ad sell more product at a good price. Also the US has a higher demand for it than for diesel.
Heavier hydrocarbons: a good portion of them are cracked to go in to the gasoline fuel product.
huh... I think you mean C9 not H9... Basic rule is that the higher the Carbon number the lesser the compression ratio it can bear(in the same homolog). It could seem a bit contradictory with the octane number, but in that the upper point (100) is 2,2,4-trimethyl-pentane. The iso-hydrocarbons can have a lot higher octane number then the normal ones: normal octane has an octane number "below zero".

I hope I did not oversimplified and that it will be understandable for someone not in the chemical industry