Usually compilers translate from the language they support to assembly. Or at most to an assembly-like language (bytecode), like GIMPLE/GENERIC for GCC or Python/Java/.NET bytecode.
Wouldn't it be simpler for a compiler translate to a simpler language, which already implement a big subset of their grammar?
For example an Objective-C compiler, which is 100% compatible with C, could add the semantics only for the syntax it extends to C's, translating it into C. I can see many advantages of doing this; one could use this Objective-C compiler to translate its code into C in order to compile the generated C code with a different compiler that doesn't support C++ (but that optimizes more, or that compiles quicker, or able to compile for more architectures). Or one would be able to use the generated C code in a project where only C is allowed.
I guess/hope that if things were working like this, it would have been a lot easier to write extensions for current languages (eg: adding to C++ keywords to ease the implementation of common patterns, or, still in C++, removing the declare before use rule by moving inline member functions to the end of header files)
What kind of penalties would there be? Generated code would be very difficult to be understood by humans? Compilers wouldn't be able to optimize as much as they can now? What else?
This is actually used by a lot of languages, through the use of Intermediate languages. The biggest example for this would be Pascal, which had the Pascal-P system: Pascal was compiled into a hypothetical assembly language. To port pascal would only mean making a compiler for this assembly language: a task a lot simpler than porting the entire pascal compiler. After writing this compiler, you'd only need to compile the (machine-independent) pascal compiler that was written in this.
Bootstrapping is also used quite often in programming language design. Many languages have their compilers written in the same language(Haskell comes to mind here). By doing this, writing a new functionality for the language simply means translating that idea into the current language, putting it into the compiler, then recompiling.
I don't think the problem with this method is really the readability of generated code(I don't sift through assembly byte-code generated through compilers, personally), but one of optimization. Many ideas in higher-level programming languages( weak-typing comes to mind) are hard to automatically translate into lower-level system languages such as C. There's a reason why GCC tends to do its optimization before code generation.
But for the most part, compilers do translate into simpler languages except for maybe the most basic of system languages.