How to set Google Chrome default profile with protractor
The core problem here is that Chrome starts a new instance every time it starts. "new" is defined by a totally separate and independent Chrome that has no idea about your 'personal' profiles. I don't think it supports that somewhat obvious customer scenario.
What it CAN do instead is save your profile data for use in future "new" instances.
See this answer from 'Isaac Lyman': keep protractor browser session alive