Alleluia (“praise Yahweh”) is an exclamation of thanks and praise. We normally sing it as a refrain to praise God for the gift of our salvation. During Lent our focus is on the journey of salvation, not the end result itself. During Lent we focus on our sins and its consequences. Throughout the Lenten season we liturgically experience the exile that sin imposes upon us and anticipate the saving death and resurrection of Jesus. So if we are spiritually and liturgically awaiting the saving actions of Jesus we would not celebrate their completion. We do that at Easter.
This “fasting” from Alleluia helps prepare us to more fully celebrate and experience the meaning of Easter.