"Do I really need to install a whole new version of Matlab? "
Yes, along with any toolboxes used by the code you need to compile.
"Why Don't matlab compilers act as standalone compilers running without the help of other compilers"
Because it is not an efficient use of resources. The code generated by MATLAB passes through optimization and linking stages, including creation of any appropriate debugging tables, and has to be compatible with the native object file format for the operating system being used. It is not efficient for Mathworks to develop their own C and C++ compilers and build them into a Mathworks product: it is much more efficient to use compilers that have been developed and debugged by other people. Compilers are not just things that translate directly into machine code: compilers also include a heck of a lot of work on header files and libraries.
As far as I can recall, each MATLAB version has always supported at least one no-charge third-party C compiler on each operating system -- SDK 7.1, XCode, gcc for example. The 32 bit MATLAB came with lcc-w32, which was not as good of an optimizer as others and which did not support parallel processing.
