What's the logic behind the word 从事?
事 can also be a verb  for 'to serve; to work for' e.g. 忠臣不事二主 (a loyal vassal does not serve/ work for two masters)
Since 从 itself has many different meanings, just say 从 is not specific enough. Adding a similar verb 事 and form the compound word 从事 make it a specific term for 'to engage in' (a field/ industry)
从政 = to undertake a political career
从商 = to engage in the business world
从影 = to work in the films industry (refers to the on-screen personnel only )
从軍 = to join/ to serve the military

从 - engage; join


事 - serve; work for


从事 = to engage in (a field/ industry)

Example:
从事环保工作 - Engage in environmental protection work
从事出入口行业 - Engage in the import and export industry