In recent years there has been a number of bills passed through Parliament (Prostitution Law Reform, Civil Union, Anti-smacking) on the basis of MPs 'voting with their conscience'. I believe it is adopted when a controversial moral issue is debated in Parliament.
Here's the problem. In the cases cited the conscience of the electorate was not represented among the MPs in Parliament. An overwhelming majority of ordinary Kiwis were opposed to the legislation.
Allowing MPs to exercise a conscience vote is undemocratic. MPs are elected to represent their constituency in Parliament (well, that's my understanding of the process). If they vote against the will of the people then they are being undemocratic.
A further problem is that under MMP there are certain MPs who are not accountable to a constituency. They get into Parliament on the party list. They do the bidding of the party and try to keep their position on the party list for the next election.
Party politics in itself is unrepresentative. The number of New Zealanders who are members of a political party is a small minority of the population. That, in itself, make party politics unrepresentative and undemocratic. There is a certain type of person who prepared to join a political party. The vast majority of the population is not prepared to participate in politics at this level. [I am not and never have been a member of a political party. If I did join a political party I would submit a remit to outlaw Political Parties and to revoke MMP.]
So whether an MP votes along party lines or votes with their conscience they are unrepresentative of those they supposedly represent. There is a serious flaw in politics in New Zealand. We do not have a democracy in the Platonic sense. Plato defined democracy as "government of the people, by the people, for the people". The propensity for politicians to array themselves in parties means we have government of the party, by the party, for the party.
Conscience voting is anathema to democracy. Political parties are anathema to democracy.