I think it's part of a general suspicion of government that has long been part of the story NH tells about itself.

The drawback is that basically all NH state politicians are constantly running for office. It's very hard for them to say "this good thing to do will piss off my supporters but it's I have time to convince people of that before the next election"

Others have answered, so I'll add my "fun NH gov fact".

Since 1900 NH has voted out the incumbent governor only three times. That's 66 elections. Sometimes the incumbent declines to run again, but when the incumbent runs for reelection, they nearly always win.

We like the chance to change our minds frequently.

'Cause we've always done it like that, since the state's second constitution was adopted in 1784. (The position was called President until 1790.) Same reason there is an Executive Council: to limit the power of the Executive. Partially in response to having the longest serving Royal Governor for 25 years: Benning Wentworth. It would take a constitutional amendment to change it, making that unlikely. Vermont is the only other state with a two year governor term. And they only switched from one-year terms to two-years in 1870.

It's insane.

Because the government should always answer to its citizens. Also thy are paid a pittance to other states so they are in it to make change, instead of being beholden to special interests