If a crosswind operation was been found to be limiting by the manufacturer then this will be published in the AFM as a ‘limit’.
Max demonstrated crosswind is not limiting, but very good advice. The value is normally published by the manufacturer in the crew operating manual. The value implies that a limit has not be encountered, but does not indicate what the margin from any limit might be, i.e. treat it as a limit. Also the wording and advice on gusts can vary.
In both cases, good safety practice recommends that operators and crews set their own lower limits according experience and situation.
Thus whilst the intent of the LIMJ statement is reasonably clear, the terminology used might be confusing. With local knowledge, operators would be expected to use a lower limit; however visitors would more likely depend on published warnings often given as a ‘cautionary’ statement. The advantage of the LIMJ ‘limitation’ is to put more emphasis on the hazard and encourage operators to reduce crosswind limits more than they might consider.
In addition, operators must consider the effects of a wet or contaminated runway where even greater reductions in crosswind should be applied, as with gusts.
A descriptive wording of a hazard is open to interpretation due to variable human performance; setting a ‘limit’ provides a strong marker-point on which to base judgement. Thus the LIMJ 'limit' is a good safety communication, it could be worded more consistently with aircraft / operational documentation.