There are two drx cycles (UE specific drx cycle and cell specific drx cycle). The minimum of these two drx are used by UE to read the paging and also min drx used by eNB to schedule the paging to UE. UE inform the UE specific drx cycle to MME via attach procedure. eNB inform cell specific default drx cycle via S1 setup request to MME.
Suppose UE specific drx cycle is different to the cell specific drx cycle. MME want to page an UE so it will send paging to UE and will send the UE specific paging drx to eNB. so that eNB can use min drx to broadcast the paging.
So i think eNB includes the default paging drx in s1 setup request to update the MME about the cell specific drx cycle so that MME can inform the UE specific drx to eNB if UE specific drx is different. Please correct me if i am wrong.