Why doesn't there exists a subi opcode for MIPS?

When you create an instruction set, you're bound by some constraints, such as the total number of instructions you can create. The MIPS creators realized that there isn't a need for subi (because you can add a negative number with addi using 2's complement), and they simply made the decision to forego making that instruction. It may have been to conserve the number of instructions, or just simply because it isn't needed.

Both addi and addiu take 16-bit signed immediates as operand, so it makes no sense to add separate subi and subiu opcodes.