Because high-end machine tools only produce basic parts, but engines require more technology. The US is way ahead of the rest of the world in terms of technology, so they can build aero engines.
America's technology is, after all, world-leading, so they leave the task of producing the basic parts to other countries. After all, Americans have a limited amount of energy, so the technologically advanced ones would certainly choose to do something more valuable. For this kind of production of basic process parts, the United States is generally given to its little brother Japan these countries to do, but it is true that Japan in the production of parts is better, is considered to be the world's parts exporting countries.
In terms of aero-engines, aero-engines have very high technical requirements. Aerospace engine technology involves a lot of fields and, so machining can only be considered the younger brother of them. But it is true that high-end machine tools can make the machining accuracy more precise, the accuracy of the parts is really also very important to the aero-engine. Machine tools are indeed important and irreplaceable in the field of manufacturing, and many important industries and technologies require precision parts to support them.
While machine tools are important, they are still basic technology. The technical requirements of the aero-engine is very wide, only the basic industrial parts is far from enough. And not only is the processing accuracy of certain requirements, aero-engine is also in the early pre-study, experiments these aspects also need to carry out important research. For example, the engine turbine, because it is to go into space, so it must be able to use the constituent materials in space, so this is not the ordinary metal materials can replace.