the cat by a clarinet playing staccato in a low register

On my reading, at least, it is not entirely true that each character is represented by an instrument, but rather by a combination of theme and timbre. Prior to the cat's appearance in the narration, the clarinet plays an accompanying role with the bassoon (grandfather, also unintroduced), accompanying the flute and oboe. It is possible that this is meant to imply that the cat and grandfather are already spying from afar, but I don't think this is a strong interpretation: the low staccato clarinet comes out with a unique timbre that keeps it distinct from the oboe and bassoon, a timbre which these early clarinet appearances avoid entirely. Representing Peter with the string quartet frees up individual string instruments to be used similarly to the clarinet in these "non-cat" passages; to be used with a different sound that doesn't put Peter in the spotlight.

The reason for these breaks from "instrument-characterization" is that the work is made up of relatively few themes that are heavily repeated, so something is needed to keep it interesting. Peter's theme is one of the most repeated, so giving him the string quartet allows for more variations, again for interest.

String instruments also sound quite similar to each other, so this solution has the added benefit of avoiding the timbrical confusion of which specific string instrument represents Peter; rather than one arbitrary string instrument that the audience may not be able to keep track of, it is the volume and range of the quartet working together that unambiguously represents Peter.

the cat by a clarinet playing staccato in a low register

On my reading, at least, it is not entirely true that each character is represented by an instrument, but rather by a combination of theme and timbre. Prior to the cat's appearance in the narration, the clarinet plays an accompanying role with the bassoon (grandfather, also unintroduced), accompanying the flute and oboe. It is possible that this is meant to imply that the cat and grandfather are already spying from afar, but I don't think this is a strong interpretation: the low staccato clarinet comes out with a unique timbre that keeps it distinct from the oboe and bassoon, a timbre which these early clarinet appearances avoid entirely. Representing Peter with the string quartet frees up individual string instruments to be used similarly to the clarinet in these "non-cat" passages; to be used with a different sound that doesn't put Peter in the spotlight.

The reason for these breaks from "instrument-characterization" is that the work is made up of relatively few themes that are heavily repeated, so something is needed to keep it interesting. Peter's theme is one of the most repeated, so giving him the string quartet allows for more variations, again for interest.

String instruments also sound quite similar to each other, so this solution has the added benefit of avoiding the timbrical confusion of which specific string instrument represents Peter; rather than one arbitrary string instrument that the audience may not be able to keep track of, it is the volume and range of the quartet working together that unambiguously represents Peter.

Of course this is all speculation, but to the best of my knowledge, Prokofiev never commented on why he chose the instruments he did; speculation is all we have.

the cat by a clarinet playing staccato in a low register

On my reading, at least, it is not entirely true that each character is represented by an instrument, but rather by a combination of theme and timbre. Prior to the cat's appearance in the narration, the clarinet plays an accompanying line as part of a wind ensemble with the flute (bird, already introduced), oboe (duck, already introduced), and grandfather (as yet unintroduced, and also only playing accompanying lines). It is possible that this is meant to imply that the cat and grandfather are already spying from afar, but I don't think this is a strong interpretation: the low staccato clarinet comes out with a unique timbre that keeps it distinct from the oboe and bassoon, a timbre which these early clarinet appearances avoid entirely. Representing Peter with the string quartet frees up individual string instruments to be used similarly to the clarinet in these "non-cat" passages; to be used with a different sound that doesn't put Peter in the spotlight.

The reason for these breaks from "instrument-characterization" is that the work is made up of relatively few themes that are heavily repeated. Peter's is one of the most frequent themes, and giving him the most instruments allows it the most variation, keeping the piece interesting.

String instruments also sound quite similar to each other, so this solution has the added benefit of avoiding the timbrical confusion of which specific string instrument represents Peter; rather than one arbitrary string instrument that the audience may not be able to keep track of, it is the volume and range of the quartet working together that unambiguously represents Peter.

the cat by a clarinet playing staccato in a low register

On my reading, at least, it is not entirely true that each character is represented by an instrument, but rather by a combination of theme and timbre. Prior to the cat's appearance in the narration, the clarinet plays an accompanying role with the bassoon (grandfather, also unintroduced), accompanying the flute and oboe. It is possible that this is meant to imply that the cat and grandfather are already spying from afar, but I don't think this is a strong interpretation: the low staccato clarinet comes out with a unique timbre that keeps it distinct from the oboe and bassoon, a timbre which these early clarinet appearances avoid entirely. Representing Peter with the string quartet frees up individual string instruments to be used similarly to the clarinet in these "non-cat" passages; to be used with a different sound that doesn't put Peter in the spotlight.

The reason for these breaks from "instrument-characterization" is that the work is made up of relatively few themes that are heavily repeated, so something is needed to keep it interesting. Peter's theme is one of the most repeated, so giving him the string quartet allows for more variations, again for interest.

String instruments also sound quite similar to each other, so this solution has the added benefit of avoiding the timbrical confusion of which specific string instrument represents Peter; rather than one arbitrary string instrument that the audience may not be able to keep track of, it is the volume and range of the quartet working together that unambiguously represents Peter.