Are German, Japanese, and Chinese companies not able to build aircraft jet engines on their own?
Well Rolls Royce designs and builds jet engines in Germany with their RR Deutschland division.  Rolls Royce Deutschland is a subsidiary of Rolls Royce and is a collaboration between RR and BMW.

The Shenyang Aerospace Corporation and Aero Engine Corporation of China are homegrown Chinese jet engine manufacturers, making their names largely for the manufacture of copies of Russian military jet engines for PLAAF need, but are now manufacturing their own designs for military and civilian applications.

Japan’s Aero Engine Corp is a partnership between Rolls Royce and several Japanese industrial powerhouses, most notably Mitsubishi Heavy Industries, who has begun to develop a line of small to medium thrust high bypass turbofan engines for regional airliners use.

While the basics of a jet engine are fairly well understood - it is, after all just a Brayton Cycle gas turbine - the details of designing and manufacturing modern high efficiency jet engines requires quite a bit of technical talent and capital to accomplish.  A new engine program often takes longer, and is more expensive than, the aircraft program it is being designed to power.  Most likely many entrepreneurs and prospective OEMs are deterred by this as any improvement they are likely to offer can be either bought out by an existing engine OEM eg Pratt and Whitney, etc. or simply crushed by the economies of scale.