This was one of the questions that was commonly posed during the early part of the stereo era, post late-1950's and onwards.
An example of a solo instrument would be the human voice. The sound comes from a small opening – the mouth – that at any practical listening distance has near-zero width, and hence has no requirement for a stereo image of any kind. There would be no point in trying to differentiate between the left side of the mouth and the right side.
So from this logic, it is pointless to use two microphones to record the human voice in stereo, one microphone in mono is perfectly satisfactory.
This is true in the context of a multitrack recording, where the voice will be combined with other instruments. Generally it is best to record the voice very close up, without any reflections from the room.
But imagine a solo singer in classical music, in church or gospel music, or a solo a capella moment in a late-night, smoky jazz club.
In these contexts, there is more to the sound than just the voice. The natural reverberation of the room plays an important part too. And since the reverberation comes from all around, it has width, height and depth, it massively benefits from stereo recording.
So although the human voice is a small instrument and in itself is not capable of generating stereo, in the context of a natural acoustic then stereo recording is essential.
Other solo instruments are large enough to generate a stereo image in their own right, regardless of the acoustics of the room.
A piano for example has a clearly audible left and right, even from quite a distance. A cello is also fairly sizeable and different qualities of sound emanate from different parts of the instrument.
Electric instruments commonly do not generate a stereo signal in themselves. Electric guitars normally have just one output and are therefore mono. It is possible to rewire the pickups and change the jack socket for a stereo socket. In this case a stereo-like sound is produced that can be interesting.
Early analog synthesizers (as an example of electronic instruments) also generally had just a single output and were therefore mono. Later synthesizers, including digital synthesizers, often had a chorus or other effect on the output which gave the illusion of stereo.
If we think about solo acoustic instruments, without the later addition of other instruments, then with few exceptions it is better to record in stereo. In the case of electric, electronic and digital instruments, it depends whether or not they produce a two-channel output.
In multitrack recording, it would be possible to try to record every individual instrument in stereo. In practice however, this gives little benefit, creates more channels to handle, and can indeed result in a more confused sound. In multitrack recording therefore it is best to decide which one or two instruments would really benefit from being recorded in stereo, and simply record the rest in mono for later mixdown to the stereo master.