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From a purely WP:LEAD point of view, the article has several sections devoted to cores and the requirement for ferromagnetism is stated prominently.  It is a reasonable summary to have the ferromagnetic core requirement in the lead.  The argument that not all ferromagnetic materials make good cores is irrelevant to the statement that all cores must be ferromagnetic.  This is the logical fallacy of denying the antecedent; all A are B is not invalidated because some B are not A.  That some new material for cores might be discovered that is not ferromagnetic is WP:CRYSTAL and also irrelevant, certainly not encyclopaedia worthy.  I am not convinced that there are any genuine electromagnet applications of air-cored solenoids.  The solenoid in its actuator role has a metal armature which is effectively acting as a core. Spark "