apt front-end is a recent addition, it was added in version 1.0 in April 2014. So it's only been part of one Debian stable release, Debian 8. People who've used Debian for longer are used to
apt-cache, and old habits die hard — and old tutorials die harder (and new users learn old habits from those).
apt is nicer for end users as a command-line tool, although even there it has competition — I prefer
aptitude for example. As a general-purpose tool though it's not necessarily ideal, because its interface is explicitly not guaranteed to stay the same from one release to the next, and it's not designed for use in scripts. Thus in any circumstance where instructions may be used in a script, it should be avoided; so it's typically safer to suggest
apt-get rather than
apt in answers on Unix.SE and similar sites.