I think piano is the quintessential instrument for classical music for a couple of reasons.
First, it is an orchestra in itself. By which I mean, a proficient musician can play multiple parts, chords and melody, percussion and song, with an amazing variety of contrasting or complementary elements. All other instruments are limited in their range and variety by comparison. Compared to piano, there are very few solo pieces written for cello or violin.
Second, because of this, it is the instrument of choice when composing. Sure, some composers played violin or cello or guitar. But they were a tiny minority compared to the number who composed at/with piano.
Third, although attaining great proficiency at piano is extremely difficult, the basics of piano and actually playing music with piano is relatively easily learned. In comparison, just sitting around the living room, singing songs accompanied by solo cello or trumpet is not exactly common. Those who play other instruments typically must play in groups with others. The end is that piano is such a familiar and comparatively common instrument, often found in homes.
That the violin is the second most common instrument for classical solo work is probably linked to piano. As a singing instrument, violin is an instrumental substitute for voice accompanying piano. It is light and portable, so can go wherever there is a piano or group to join with. It can be played loud enough to be heard with piano. And audiences can easily appreciate the voice of the violin.
Cello was a more recent addition to the classical instrument family. Even into the mid-1700s, the bass violin was the instrument of choice in this voice range. So there is less history of writing for it as a soloist instrument. But since the 1700s, there have been quite a few concertos and other works for cello and orchestra originating with pieces by Vivaldi and Boccherini, I suppose. And actually, there have been quite a few modern works for cello and orchestra.
Although there are not many works for solo cello, there are a few substantial contributions. Other than the ubiquitous Bach cycle, there are modern works by Kodaly, Britten, Ligeti, Carter, etc.
I doubt the cello will ever have the same appeal as violin, though. A lot of people do not really like its dark, sinister side, and it can sound lead-footed and unmusical as a singing instrument in all but the most expert hands.
Personally, though, I love cello in chamber music, which it where it can have a prominent role with solo segments that complement piano and violin beautifully. I personally enjoy cello sonatas (accompanied by piano) more than I do violin sonatas.
Not sure this is really responsive to the original post, but .....