The problem is, very succinctly, that they don't really belong in violin recitals, but they are never heard in piano recitals.
Why is this? These lovely pieces of chamber music were not written for violin with piano accompaniment, but rather for piano (fortepiano, actually, the predecessor to the modern steel-frame piano) with violin accompaniment. Both Mozart and Beethoven wrote them for themselves to play, the keyboard part, that is, with another musician playing the violin part. The greater weight is in the piano, which is why it would be nice to hear them in a piano recital. But, due to economics as much as anything else, we never hear them in piano recitals, but only in violin recitals.
I heard one last night, a violin recital that is, and the first item on the program was the Beethoven "Spring" Sonata for piano and violin. Here is how that goes:
I think you can hear the nature of the composition in the first 50 seconds, leading up to the first big cadence. There is a nice, charming statement of the basic theme in the violin, followed by a much more elaborate version of the theme for piano. Cadence. Last night, as you would hear it handled in most violin recitals (where the violinist is the star), we heard a nice charming theme, beautifully played, followed by a much longer section of accompaniment figures, also beautifully played, while slightly in the background the considerably less stellar pianist struggled with his more virtuoso part. You see the problem? This is not a violin sonata with piano accompaniment, it is, rather, a piano sonata with violin accompaniment. The pianist doesn't want to sound overbearing so he underplays the piano part. The result is unsatisfying.
Now, this can be done well, of course, but the pianist needs to be very, very good and the violinist has to not think of themselves as the big (or only) soloist. Here are Hilary Hahn and Natalie Zhu showing us how it's done:
After Beethoven the changes in musical culture in the 19th century changed the character of the violin sonata and it became more a violin sonata with piano accompaniment. The parts became more equal and then the violin became more predominant. Let's listen to some Brahms for an example:
No question there that, at least in the first part, the violin gets all the tunes, occasionally joined by the piano, who mostly plays accompaniment figures.
The reason Mozart and Beethoven wrote their unusual piano sonatas with violin accompaniment was likely due to several things: first of all, chamber music was a popular pastime for a lot of amateur musicians and there was a ready market for the scores. There were a lot of amateur pianists and amateur violinists around and probably more competent players of the former. Also, as I said, both Mozart and Beethoven wrote these sonatas for themselves to play on the piano (though Mozart could have played either part). The other reason may have had to do with the sonority of the 18th century piano. Frankly, it did not have the long sustain, especially in the higher register, of the later piano. High notes tended to sound clunky and short. The violin could really help in this regard. You might be able to hear what I mean in this performance of a Mozart sonata on original instruments:
It would be great to hear these pieces in a piano recital but the current model for those was set by Clara Schumann and Franz Liszt and they are almost always a case of the romantic figure of the lone pianist sharing the stage with no-one.
There is another repertoire that shares this problem and that is the trios for violin, piano and cello by Joseph Haydn. Lovely pieces, but the cello is really there just to augment the bass line of the piano, though the violin gets a bit more to do. Again, the three instruments are not treated equally and the piano is very much the most important.
All of this repertoire fits awkwardly into our current recital models. The soloist pianists don't want to play it because they don't want to share the stage (or the fee), but at the same time it is not ideal for chamber music series either as our model for chamber music is that all the parts have to be democratically equal. Pieces where the piano is the lead, accompanied by one or two string instruments, just don't make any sense to us! Mind you, these sonatas do fulfill the minor function of being good opening pieces in a violin recital, soon to be followed by weightier ones. This was the function of the Beethoven sonata last night. But it resulted in me making the shocked remark that the best piece on the program was Tzigane by Ravel! And since when does Ravel beat out Beethoven?
Nothing wrong with these early sonatas for piano and violin, by the way. Lovely music. But as I say, perhaps better suited to a piano recital than a violin recital--not that we will ever hear them there.
Let's end with another one, this is the Mozart Sonata in E minor:
Incidentally, we can see the shift from the 18th century model to the 19th century one, where the violin takes on much more weight, as early as the Beethoven Kreutzer Sonata, that begins with a violin solo:
So there you have it. There is a lot of repertoire from the past that is really great music, but that does not fit well into our fundamentally 19th century recital formats. One thing that the Early Music movement has done is revive a lot of music that was not well known and provide a somewhat different context for some of it that we thought we knew.