The debate about the choice between playing the trumpet or cornet has been going on since the trumpet switched from low F to mezzo Bb around the turn of the 19th/20th centuries. Louis Armstrong switched to trumpet in 1927 when he started playing in a dance band, and it seem to have been the dance bands that promoted the trumpet.
In this article by Nat Gonella from 1933 he points out that it is the streamline look of the trumpet as much as its greater projection that makes it more suitable for "modern" music.
Click here to read it online.
(From Modern Style Trumpet Playing by Nat Gonella, Henri Selmer & Co, 1933)