Why do few examples of Phoenician writing still exist

Because it left a mark on modern letters.

Explanation:

The Phoenician script originated around 3000 BC. The Phoenician script is based on the North Semitic script. Many nations such as Greeks, Syrians, Jews, Arabs, and others made their letters based on the Phoenician script. Because of the fact mentioned above, the Phoenician script has left such a strong footprint and influence on other scriptures. Like the Hebrew and Arabic scripts, the Phoenician script has no vowel signs. Each sign represents one consonant, and the vowels are pronounced according to the meaning.