Ciao Andrea, yes somehow you would be right to use the "plus que parfait" if you would write "le lecteur AVAIT EU" (avait eu = "plus que parfait") since le plus-que-parfait—is used to indicate an action in the past that occurred before another action in the past. But here you need to use the "Conditionnel passé" = AURAIT EU to describes an event in the past that is not guaranteed to occur, this event which is dependent on another condition to occur, hence the use of the CONDITIONNEL PASSE.The French conditional is mainly used in if...then constructs.
The past conditional, is a compound conjugation, with these two parts:
+++ conditional of the auxiliary verb (either avoir or être) = AURAIT (in the exemple)
+++ past participle of the main verb = EU (past participle of the verb AVOIR)
The French past conditional, is usually used very much like the English past conditional: It expresses an action that would have occurred if past circumstances had been different.