Max Kaminsky was probably more highly-regarded amongst peers than jazz fans, lacking as he did the sheer fire of Wild Bill Davison or the romanticism of Bobby Hackett. However, he was an expert at playing an economical yet swinging melody.
Playing a melody well is one of the most difficult things a jazz musician can attempt - it's relatively easy to play an unimaginative improvised solo that will fool casual listeners. Embellishing a melody means one has set material to work with, less room to deviate, and probably other horn players with whom to jostle for space between the barlines.
Kaminsky's no-fuss lead lines did more than state melodies - they inspired his fellow musicians. It's no wonder 'thinking trumpeters' like Tom Baker, Roger Bell and Ade Monsbourgh loved his playing (he visited Australia with Artie Shaw's band during World War II, hence his strong influence on Australian musicians).
Here's a great video clip with an all-star lineup including Herb Hall on clarinet, Stuff Smith on violin and George Wettling on drums:
And here are two records that show Kaminsky at his early peak: