Why would I level up Assist Units?
Their stats are added to the character that you have them set to assist.
By this token, you should consider to use high STR assist characters with your characters that use STR, etc.
Since leveling up a character increases its stats, it is beneficial to level up your assist characters.
Here is an example:
The strength starts at 51. Hestia's 23 strength is added for a result of 74 strength.