I think part of the problem with that is just how far away Neptune is.
Getting a probe like New Horizons to do a flyby requires a massive rocket. But to also have it be capable of slowing down to enter orbit and stick around means either it was moving slower on it's path to get there (so it takes a lot longer) or it has to carry a huge amount of fuel to burn to slow down (so it takes an even bigger rocket).
So for any of these destinations there are really two options: fly-by or orbit insertion.
Pluto obviously was a fly-by. There were several reasons for this. Distance is a big one. Also, the more distant planets are the lower their orbital velocity. More distance = longer travel time. A higher velocity can reduce the travel time but you need to speed up at launch and slow down on arrival and that requires a higher delta-V budget. That requires extra mass of fuel, which becomes a vicious circle.
Pluto is tiny and far so a fly-by was really the only option. Even then it took 10 years to get there.
Neptune is more massive, closer and heavier. All of these help but if I'm reading [1] correctly, you'd still be realistically looking at a 30 year travel time for an insertion orbit. Having instruments hibernate for that long and work on the other end is really the biggest problem.
We're entering an era of super-heavy lifters. Maybe these will meaningfully increase the practical delta-V budgets.
Inserting a probe into orbit around Uranus (let alone Neptune) seems currently impractical just given how long it would take but that doesn't make me want it any less. Even a fly-by is better than nothing.
But the delta-V for Saturn, Uranus and Neptune are all roughly the same
Getting a probe like New Horizons to do a flyby requires a massive rocket. But to also have it be capable of slowing down to enter orbit and stick around means either it was moving slower on it's path to get there (so it takes a lot longer) or it has to carry a huge amount of fuel to burn to slow down (so it takes an even bigger rocket).
Neither option is great.