I am beginning to read some UC framework papers, and I guess it is similar to the simulation-based security analysis. I can understand the main advantage of UC is to assist us to analyze the composable protocol. But I am wondering what are the main limitations of UC? I note that it is non-trivial to transform simulation-based security (or game-based security) into UC security. But does there exist compiler to transform form simulation-based security to UC security.
"Simulation-based security" is a very general notion. UC security is much more specific - it refers to a simulation-based security proof in the UC framework. As such, simulation-based security encompass the UC framework, which is a particular case of it, and there is no general transformation from any primitive with a simulation-style security argument to a UC secure primitive.
One of the main limitations of the UC framework is that it's strength - arbitrary composability features - also gives rise to strong impossibility results: many important cryptographic primitives are provably impossible to realize with UC-security in the plain model, hence one must rely on trusted setup assumptions, such as the common reference string model, to build protocols in the UC framework.
Arguably, a second limitation is the relative complexity of the framework, which is not so easy to understand and master in depth - although there are now countless examples of proofs in the UC model to look at, as well as simplifications of the model such as simple UC.