An alias also seems like it'd work.
alias egrep='grep -E'
alias fgrep='grep -F'
alias egrep='grep -E'
alias fgrep='grep -F'
When bash is called as /bin/sh, it will be in POSIX mode, and will honor those aliases.
When called as anything else or when otherwise not in POSIX mode, those aliases will fail.
Bash was around for a decade before the POSIX shell standard was defined, so there is legacy baggage.