We are blinded to the impact of Louis Armstrong's recordings between 1925 and 1928. Their impact is simply so pervasive that it is almost hard to conceive what music was like before them. There isn't a phrase of modern music that doesn't owe at least some of its influence to Louis Armstrong, and the Hot Five's and Hot Seven's in particular. It is difficult to understand what improvisation or soloing was before these albums were recorded. They are easily some of the most influential recordings on the planet!
In the years between 1925 and 1928 Armstrong recorded 79 tracks that are responsible for the trajectory of American popular music. These recordings include Potato Head Blues, Muskrat Ramble, Mahogany Hall Stomp, Heebie Jeebies, Muggles, and Struttin' With Some Barbecue. Throughout these three years, these recordings established the improvised solo as a chief focal point in jazz. It shifted the focus from the collective improvisation to something more individual. Armstrong's succinct and inspired solos set a standard for individual expression that musicians have strived for ever since.
Of all of these recordings the most influential is likely West End Blues. Recorded towards the end of this run it also featured highly arranged ensemble writing which set a template later used by swing era arrangers. Armstrong's opening cadenza was seen as a technical marvel for its time, and his singing on this, and on tunes such as Heebie Jeebies, popularized the idea of scat singing.
My personal opinion is that these recordings don't get listened to enough for a very basic reason - the recording quality. It is hard to get past the older recordings and into the amazing music that is being captured. We have to get past that. We have to embrace some of the fuzz and hiss on the recording in order to appreciate the gold in the music that is being captured - because for music - Armstrong's Hot Five's and Hot Seven's are the Mona Lisa!