While some people can make a big impact behind the scenes, it was announced well before his take over that this would happen.
There comes a time where you need to evaluate what kind of value you bring to the table and have some foresight.
Not to say it is nice to see people laid off and out of work, but from the perspective of taking ownership of your life and your career, you need to be prepared for the worst case scenario and act accordingly. Like you said, at a large “corporate America” company you are likely just another cog in the wheel outside of the team you regularly interact with.