What is the motivation for using S-TMSI in paging message instead of M-TMSI?

Hi Experts,
As you know, network uses S-TMSI (MMEC+M-TMSI) as UE identity in paging.
Considering the fact that M-TMSI is unique within an MME, why can’t the paging identity be M-TMSI? What benefit are we adding by including the MMEC too to the M-TMSI here?

In Short:
to ensure that the MMEC is unique within the MME pool area and, if overlapping pool areas are in use, unique within the area of overlapping MME pools.

The S-TMSI is used to protect the subscribers IMSI during NAS interaction as well as identifying the MME (Mobility Management Entity) or MME pool that is responsible for the UE. The S-TMSI is constructed from the MMEC (MME Code) and the M-TMSI.