Systems demand that certain primitives be aligned to certain points within the memory (ints to bytes that are multiples of 4, shorts to bytes that are multiples of 2, etc.).
GCC is smarter than most of us in producing machine code from our source code; however, I shiver if it was smarter than us in re-arranging our structs, since it's data that e.g. can be written to a file. A struct that starts with 4 chars and then has a 4 byte integer would be useless if read on another system where GCC decided that it should re-arrange the struct members.
Structs are frequently used as representations of the packing order of binary file formats and network protocols. This would break if that were done. In addition, different compilers would optimize things differently and linking code together from both would be impossible. This simply isn't feasible.
gcc SVN does have a structure reorganization optimization (-fipa-struct-reorg), but it requires whole-program analysis and isn't very powerful at the moment.
C compilers don't automatically pack structs precisely because of alignment issues like you mention. Accesses not on word boundaries (32-bit on most CPUs) carry heavy penalty on x86 and cause fatal traps on RISC architectures.
You might want to try the latest gcc trunk or, struct-reorg-branch which is under active development.
https://gcc.gnu.org/wiki/cauldron2015?action=AttachFile&do=view&target=Olga+Golovanevsky_+Memory+Layout+Optimizations+of+Structures+and+Objects.pdf
Not saying it's a good idea, but you can certainly write code that relies on the order of the members of a struct. For example, as a hack, often people cast a pointer to a struct as the type of a certain field inside that they want access to, then use pointer arithmetic to get there. To me this is a pretty dangerous idea, but I've seen it used, especially in C++ to force a variable that's been declared private to be publicly accessible when it's in a class from a 3rd party library and isn't publicly encapsulated. Reordering the members would totally break that.