ANSWER: Because they're not a kind of storage cell.
Step-by-step explanation:
However, they do contain starch, at least in their chloroplasts during photosynthesis or maybe in some vacuoles, importantly only for a short time. But it'd be correct to say that they don't formally contain starch, because they're a kind of photosynthetic (meaning productive) cell; and the starch they produce and keep temporarily will later on be sent to the storage cells such as those paranchymatic ones in root or stem (and generally in special plastid organelles called amyloplasts) or maybe fruits if present.
Though, it may be significant to note that it'd be wrong to undoubtedly say mesophyll cells don't contain starch. They do and one can determine its presence in leaf cells by trials with indicators for starch like iodine.