It's not about efficiency -- it's about correctness. basename uses newlines to delimit the filenames it prints out. In the usual case when you only pass one filename, it adds a trailing newline to its output. Since filenames may contain newlines themselves, this makes it difficult to correctly handle these filenames.
It's further complicated by the fact that people usually use basename like this: "$(basename "$file")". This makes things even more difficult, because $(command) strips all trailing newlines from command. Consider the unlikely case that $file ends with a newline. Then basename will add an extra newline, but "$(basename "$file")" will strip both newlines, leaving you with an incorrect filename.
Another problem with basename is that if $file begins with a - (dash a.k.a. minus), it will be interpreted as an option. This one is easy to fix: $(basename -- "$file")
The robust way of using basename is this:
# A file with three trailing newlines.
file=$'/tmp/evil\n\n\n'
# Add an 'x' so we can tell where $file's newlines end and basename's begin.
file_x="$(basename -- "$file"; printf x)"
# Strip off two trailing characters: the 'x' added by us and the newline added by basename.
base="${file_x%??}"
An alternative is to use ${file##*/}, which is easier but has bugs of its own. In particular, it's wrong in the cases where $file is / or foo/.
csh. I guesscshis not POSIX then.