Why can a single Sumerian cuneiform sign have several sound values?

A single Sumerian cuneiform sign can possess multiple sound values due to the nature of the script as a word-syllabic system, which evolved from logographic origins.1

The primary reasons for this include:

• Polyphony: Because a logogram often represented several related concepts—such as "sun," "day," and "bright"—the sign could be associated with the different names for those concepts, thereby assuming multiple phonetic values.1
• Rebus Principle: To represent abstract ideas or proper names, the Sumerians used signs to evoke a sound rather than the original object depicted. For example, a sign representing "hand" (šu) could also be used to represent the phonetic syllable šu in any context.1
• Homophony: The Sumerian language contained many words that sounded identical. Consequently, several different logograms could yield the same phonetic value, leading to a system where signs were distinguished in modern transliteration by numerical subscripts (e.g., ba, bá, bà, ba₄).1

These features allowed the script to function as a flexible, albeit complex, system for recording both concrete objects and grammatical elements.1