This may be one competing definition among several, but I don't think it's the most widespread.

If you use that definition and plug it in to arguments where some other definition is intended, I don't think the arguments are going to make much sense.

In particular, it's very often used (by people who use the term disparagingly) to mean a reflexive anti-intellectual attitude (and among the reasonably affluent and college-educated, no less).

In order to have mutually comprehensible conversations, I think the diversity of meanings has at least to be acknowledged, though it's fair to argue that one meaning ought to be considered the correct one (e.g. due to coherence with historical usage).