What are the advantages of this over a simple function with the following signature?
uint32_t read_big_uint32(char *bytes);
Having a big_uint32_t type seems wrong to me conceptually. You should either deal with sequences of bytes with a defined endianness or with native 32-bit integers of indeterminate endianness (assuming that your code is intended to be endian neutral). Having some kind of halfway house just confuses things.