A related idea - if the circuitry around all 8 (16-bit registers) is the same...I'd wonder if the '386 might actually have 8 segment registers - 6 user-accessible, and 2 more reserved for the microcode. The latter mostly used when navigating some of the more "interesting" states transitions which the '386's paging / protection / segmentation architecture allows.
The microcode hardly needs the segment selector registers. It uses the descriptor cache which includes the base, limit and access rights of the 6 segments + GDTR, IDTR, LDTR and TR. The descriptor cache is update by the MOV to segment and L{GDT,IDT,LDT,TR} instructions.