I know many banks still have AIX systems with shells like ksh89, ksh93, etc. as the default shell. So if a shell script is written to work with a POSIX shell (instead of a particular shell), it has a better chance of running on such systems.
Also, on Debian, the default non-interactive shell is dash [1]. This is the Debian Almquist Shell (dash). It is a POSIX-compliant shell derived from ash. So again, if we write system scripts for Debian and want it to run on Debian without any hassle, it makes sense to write the system scripts to conform to POSIX shell. Although shellcheck cannot perform full POSIX compliance check at this time, it is still a pretty good tool that can help with checking compliance with dash in particular.