The primary "argument" for longer terms is that they would let government "get more done", either by insulating them from electoral pressure (an explicitly anti-democratic argument) or just by giving them more time to consider policy and bed in change. And it occurs to me that the best argument against this is this Labour government. They were elected with an absolute majority, giving them the power to do anything they wanted. But look at how little they've done. Look at what they've chosen not to do. Can anyone really argue with a straight face that they'd "get more done" if they were less accountable to the electorate? That the real barrier to them acting on inequality or housing or climate change has been lack of time, rather than lack of interest? Really?
Labour didn't rule out a capital gains tax because they lacked time to implement one. They ruled it out because it is not in their class-interest as highly-paid, wealthy property owners. They haven't dragged their feet on climate change because of lack of time - they're doing it to protect the status quo. And they haven't refused to reverse the 1990 benefit cuts or cancel WINZ debt because of lack of time. They've ruled those things out because at the end of the day they don't care and don't want to be seen as being nice to the poors.
Rather than "getting more done", if given a longer term, this government would just sit on its arse collecting its inflated salaries, while making excuses for its political choices and trying to gaslight us into thinking that everything is great. And laughing at us all the while for being fool enough to make them less accountable.
(And on the flip side, if they were a government which did things? Yeah, we want an opportunity to vote that shit out as quickly as possible, because we might not like it. Just think of what Roger Douglas or Ruth Richardson could have done with an extra year... Aren't you glad voters could nobble them when we did?)
As mentioned above, if you like a government and think it deserves more time to implement its policy programme, vote for them at the next election. But don't surrender control or allow them to be less accountable. Because that will lead to worse, less responsive, and more arrogant government, while benefitting no-one but the politicians.