Can you clarify your question? Are you talking about Chopin etudes in particular, or about etudes in general?

It's important because Chopin wrote his etudes not only with the training aspect in mind but also took care to make them sound appealing. That's why they have melody lines, interesting harmonic progression and other aspects that make them proper pieces of music. That's why we listen to them. You wouldn't listen to Hanon or Czerny for entertainment, which are just a bunch of finger exercises chained together.

So this is bound up with the history of the piano and piano sets in general.

Chopin's etudes were composed and compiled alongside the sets of Preludes, and were explicitly written to cover all keys. This obviously harkens back to Bach's sets of Preludes and Fugues in all keys, that is, the Well-Tempered Clavier. If we look at the frontmatter of this work, we see the following inscription,

The well-tempered Clavier, or Preludes and Fugues through all the tones and semitones, both as regards the tertiam majorem or Ut Re Mi [i.e., major] and tertiam minorem or Re Mi Fa [i.e., minor]. For the profit and use of the studious musical young, and also for the special diversion of those who are already skilful in this study, composed and made by Johann Sebastian Bach, for the time being Capellmeister and Director of the Chamber-music of the Prince of Anhalt-Cothen. In the year 1722.

Notice how Bach specifies that this is for private use. It is to help train "the studious musical young" both technically (these are hard pieces!) and creatively by providing them with good compositional models to emulate. It is important to remember in this regard that studying music meant studying how to compose as well as play back in the eighteenth century. But note also that training is not their only value. They are intended to delight mature musicians as well. In other words, they serve two functions, training and delighting

But Bach obviously also did not intend for these to be heard in concert. He expected that the people that would enjoy this would be the ones playing it. This is because there really wasn't a public music scene for solo pianists in the eighteenth century. Public music consumption consisted of things like operas, church going (ie, organ and choral music), and, later, things like symphonies and concertos. So there was simply no audience for solo keyboard music. The audience was the players, delighting themselves in private.

Now, one of the great stories of the 19th century is the emergence of the piano as a public instrument. This happened very gradually. By Beethoven's time, solo piano music could be incorporated into public concerts, but they could not hold the attention of an entire evening. Instead they served as small sections within a multimedia event, decked out with symphonies, concertos, arias, and so on. The solo piano did find an audience in small "soirees" all throughout the 19th century, which were small in scale, and still featured several different kinds of pieces (not just solo piano), but they resemble something much closer to what we think of as a modern recital.

And in this context, Chopin's etudes certainly were performed. In fact, they were even performed by Chopin himself. Here is a Chopin concert program from 1848, with the Etudes fitting into the third slot. It's also true that at least some of these Etudes appeared in publications dedicated to pedagogical materials, like this one: https://imslp.org/wiki/Méthode_des_méthodes%2C_Op.98_(Moscheles%2C_Ignaz)

So with Chopin's etudes, we are seeing a genre in transition, just as we are seeing an instrument in transition. Pieces in this vein were never exclusively meant to be mindless exercises (well, some individual examples may have been, but not the whole genre). They have always had some aesthetic value (though aesthetically valuable pieces are still useful for training budding composers). But over time, the term etude took on less of a sense that it was pedagogical, and more of a sense that it was a technically difficult piece. By the time we get to, say, Rachmaninoff's etudes tableaux, then I think there is very little of the original pedagogical spirit left in the genre. "Study" has transformed from "piece to be studied" into "piece that shows off how studied you are." Chopin's etudes sit somewhere in between. They aren't necessarily stepping stones to more difficult pieces, they are crowning achievements within one's training, a sort of "play these and you can play anything" sort of thing.

There's a kind of misleading assumption here, that Chopin wrote the Études as preliminary or preparatory to something else, rather than as a complete and self-contained masterwork. At the time they were written, these Études represented the most challenging collection of technical passages ever assembled in the piano literature. Sure, certain pieces by Beethoven (looking at you: Op. 106 'Sonata für das Hammerklavier') may represent a unique challenge in sheer scale and physical-psychological stamina, but no pianist had quite written such innovative and elaborate instrumental choreography that ALSO contained a genuinely artistic and beautifully musical sense of form and expressiveness. Certainly Chopin learned much from pianistic predecessors like Clementi, Field, and Hummel - as well as the new type of extreme virtuosity created by Paganini on the violin.

His achievement here is similar to Paganini's in fact - the Études do for the piano what the Caprices of Paganini do for the violin. They throw down a gauntlet that challenges all other performers to rise up to it, representing a new standard of achievement and mastery of the art. They create the possibility for evolution and transcendence of artistic and athletic limits, to confront challenges that some might say are impossible. Paganini's "impossible difficulties" were unequaled in his day, they are now standard repertoire for aspiring violin soloists. Chopin likewise was criticized by respected contemporaries like Ignaz Moscheles, who found "unplayable passages" filled with "bizarre harmonies". Of course, Chopin found supporters in the younger romantics Schumann and Liszt. Chopin dedicated the Op. 10 Études to Liszt, who sightread the work in front of the (undoubtedly awestruck) composer. Chopin exclaimed that he "would like to steal [from Liszt] his way of playing my own Études." Liszt and Schumann would go on to compose their own Études, advancing the genre while still being strongly influenced by the virtuosity of both Chopin and Paganini.

The question of how the Chopin Études, and Études in general were received by the contemporary public, is therefore a double-edged sword. This new type of Concert Étude, as exemplified by the Paganini Caprices and the Chopin Études, was certainly intended to be heard and enjoyed by audiences - as evidenced by the public programming of these works by the composers. Contemporary music journals and personal diaries of concert goers describe the incredible impact these performances had on their audiences. However, the audience of the published works - the notated scores - must have been much more limited due to the extreme difficulty of the works themselves. Music published during the earlier period of Mozart, Haydn and Beethoven was largely intended for consumption by amateurs. A widely educated and literate musical public was quite expected to read and perform these works in private chamber concerts. This was no longer the case with the concert works of Chopin and Liszt, which were reserved only for the personal conquest of the great virtuosos that wrote and performed this music to a rapt public audience. That others might also learn and perform this music was an ambition only for the extremely gifted, the price of entry is nothing less than genius.

I think the better translation for the French word "etudes" is "studies,' not lessons.