Yes but if each house district is FPP 3rd parties generally don't get a look in, people who vote for them get no representation at all, and can produce governme

Yes but if each house district is FPP 3rd parties generally don't get a look in, people who vote for them get no representation at all, and can produce governments where the party with the most seats got fewer votes than the others. MMP provides local representation, and proportional representation (at the expense of having larger local seats, or more representatives).