In ELF-header, value of e_ident[EI_CLASS] can either be 1 or 2, which indicates 32-bit operating or 64-bit operating system. But from history we know that ELF first appeared in Solaris 2.0, which is released in 1993. However, widely used 32-bit processor Pentium Pro didn't appeared until 1995.
So why does ELF header has no information about 16-bit or even 8-bit information?
The first "widely used" 32-bit CPU was the Intel 80386 which was much older.
Then we have the story about SUN and their SPARC architecture from around the same time-frame as the 386.
Solaris was developed by SUN for their machines in the early 1990's, close to when the first 64-bit systems started appearing actually.
ELF (acronym for the Executable and Linkable Format) was developed in the late 1980's, when all major Unix variants ran on pure or hybrid (think Motorola 68000) 32-bit systems.