Traditionally in x86, only the first byte is the opcode used to select the instruction, and any further bytes contain only operands. Thus, since there exist 256 possible values for the initial byte, there are at most 256 possible opcodes to represent different instructions.

So if you add a 1-byte instruction for each register to zero its value, that consumes 8 of the possible 256 opcodes, since there are 8 registers. Traditional x86 did have several groups of 1-byte instructions for common operations, but most of them were later replaced with multibyte encodings to free up space for other instructions.