NASA hasn't made their own engines in a few decades. It's been all contractors for quite some time. Without NASA the private sector wouldn't have been able to capitalize manned space flight.
Actually, I don't believe NASA has ever made its own engines or spacecraft. Even going back to the late 1950s when NACA became NASA, the hardware was almost exclusively designed and produced by contractors such as Douglas, Boeing, Grumman, North American, etc.