Or phrased in a slightly less inflammatory way, someone on Deskthority speculated (and I agree that this is highly plausible) that SA profile might have originally been intended for some type of keyswitch with a tilted stem.
As evidence, here’s a diagram superimposing SS Family profile on top of SA profile with each SA cap rotated 11°:

Check out this nice photo of a beam spring board from Halvar on Deskthority. Note how the keycaps look basically like SA, but are mounted at an angle to the beam spring switches, giving them a much nicer profile:

Edit: I wonder if SA stands for “spherical
angled”, with SS standing for “spherical
straight” (or maybe “spherical
scupltured”).
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Update:Daniel Beardsmore directly asked SP about this, and got the following reply from them:
The first keycap family produced by Signature Plastics’ previous company, Comptec Inc., was the SA family. These keys had a Spherical touch area and the same profile for All rows.
A few years later the company began producing the SS family which also had a Spherical touch area but with a Sculptured profile i.e. each row had a different keycap angle giving the keyboard a curved look. Because of the limited number of shapes that were tooled, this tooling has been retired and is no longer available for production.
In the mid 80’s an attempt was made to standardize keycaps to a ‘DIN Standard’. DIN stands for “Deutsches Institut für Normung”, meaning "German institute for standardization". This resulted in a new high profile family being produced, the DSS family, which was a DIN standard, Spherical touch, Sculptured key family. This family profile was never very popular and was quickly retired. A short time later the SA family was re-tooled to produce a sculptured look. The keycap family name didn’t change, but it was simply referred to as sculptured SA.
The fourth family tooled was the low profile DSA family. These keys met the DIN standard, had a Spherical touch area, and the same low profile look for All rows.
The DCS family followed shortly. These keys conformed to the DIN standard, had a Cylindrical touch surface, and a Sculptured profile.
The latest keycap family, introduced by Signature Plastics in 2015, is the G20 family. These keys were designed with the gaming community in mind. They have a flat touch area that is wider than standard keycaps, resulting is a smaller gap and easier transition between adjacent keys. These keycaps have the same angle for all rows, similar to the DCS R2 profile.
In short:
SA = Spherical All-rows
SS = Spherical Sculptured
DSA = DIN-compliant Spherical All-rows
DSS = DIN-compliant Spherical Sculptured
DCS = DIN-compliant Cylindrical Sculptured