For game engines, point #3 is the most important. JIT compilers tend to do better when the entire codebase is in the same language, because they can't optimize

For game engines, point #3 is the most important. JIT compilers tend to do better when the entire codebase is in the same language, because they can't optimize code that is written in C/C++, and have a harder time optimizing code that calls C/C++. However, this is exactly the sort of thing at the core of a game engine. Another thing is that when making games a scripting language can be easier to use by members of the team who may be good at game design but not good at programming in C++. It is also convenient to be able to edit the scripts without needing to recompile and restart the game. In the case of Lua, one thing that makes it popular for games is that it is very small and also easy to embed. It was designed for ease of embedding.