Back in its day it was pretty popular, but I think we view it today with a collection of other cartraiges like the 357 mag or the 357 sig.
Now step into the way back machine and think about it. When the 38 super came out you had in the states, the 38 special, the 44 special, 45 colt as the big revolver rounds, you had the 45 acp, 380 auto and 25 auto along with the 38 auto as the big autoloader rounds. I discount the 9mm because my research seems to indicate these were pretty rare in the states back then. Also the 30 lugar, 455 and others were again rare.
So if you wanted a high speed round, the 38 super was it prior to the 38/44 in april of 1930.
When did the 357 mag come out? 1935 in May?
To me the weakness of the 38 super was always the accuracy/headspace issue and that was not "practically" solved till the late 70's or so. Had Colt headspaced the round correctly, lopped off the semi-rim and stayed with the original power levels, I have to wonder if the Super would have supplanted the 45acp in the american shooter psyche. I know as a kid, I always looked at the ballistics tables and wondered why the 45 acp was the "thing" to get when compared to the 38 super, but back then not many folks understood the accuracy issue. I know I certainly did not.