this isn't really true. To change companies you might need to move cities, but there are a ton of different companies that require aerospace engineers:

SpaceX Blue Origin Space Systems Loral JPL Boeing Embraer Airbus Cessna Northrup Grumman Lockheed Martin General Electric Raytheon Boom Rolls Royce, Honeywell Eurocopter Bombardier

not to mention the adjacent fields of Green tech (wind turbines) Drones/UAVs

There are a lot of options out there