Why is the program header executable?

The PHDR pointing to the PHDRs tells the loader that the PHDRs themselves should be mapped to the process address space, in order to make them accessible to the program itself.

This is useful mainly for dynamic linking.

The reason the memory is marked as executable is because the PHDRs are smaller than one page, and live right next to the start of the executable code. If the permissions for the PHDRs were different from those of the program text, the linker would have to insert padding between them.