We can't afford to play guys who may eventually come good, Santner offers little with bat and ball atm. He'd be better off working on his game at the domestic level before giving another run in Tests.
As for Guptill, I want to see what Guptill can do against the older ball at 5. It was poor to have him open when it's evident that he struggles to playing the moving ball.
Neesham is self explanatory, I'm surprised he isn't playing here. IIRC he scored 70 odd in the last Test he played in India, looked great while scoring those runs too.
Name someone who can do the job Santner has done for the past 12 months in tests though, I think Williamson should definitely bowl himself more, but Santner has taken wickets at 38, kept the runflow reasonably quiet and done so in conditions that don't usually offer him that much, and that's in his debut year. His batting needs to come on more, but bowling wise, take a look at the returns of Craig, Sodhi, Jeetan, Nethula, Astle etcetera to see why you just can't leave Santner out.
Also, the "Let him go get better at domestic" doesn't really work in NZ - captains do not know how to use spin here, pitches don't support spin here and they just don't progress unless they're in the national team or playing county style cricket.
Guptill won't get a chance at five, unless he does what Brownlie tried to do (and failed) and move himself there for Auckland and show over the course of a few seasons that he's worth a go. He's burnt his chances and to be honest, I'd rather see us promoting youth, there are quite a few prospect batsmen showing up, there are only so many times you can say "Well Guptill is so naturally talented" but to look at his record, he's just not shown it, ever.