30 years ago: Voyager 2's historic Neptune flyby

Because it's a mostly unexplored corner of our solar system. The Voyagers were survey probes: they saw glimpses of a lot of interesting things, but couldn't stick around and solve any of the hard mysteries. (For example, just what is going on with the weather on both Uranus and Neptune? It's weird!) Orbiters such as Galileo, Juno, and Cassini are able to stick around long enough to do deep science.

Orbiters for one or both of our ice giants ought to be much higher on our space exploration priority lists than they seem to be.

Because the 10-year-old me was teased with pictures and mysteries I want answers to. Because it’s so far. Because it can’t see more than a pale dot in my telescope. Because it’s so alien. And because we have been there, done that on everything you mentioned.

Perhaps if I’m ever granted the opportunity to present my case before NASA and Congress, I might offer a more well-thought-out explanation. But right now, “because it would be awesome” should suffice.

Setting aside the feasibility of solar sail propulsion, power will be an enemy: just getting a typical cubesat level of 5W is much harder at Neptune, since Neptune gets just 1/900th the solar flux. By way of comparison: the "Juno" probe produces 486W at Jupiter (solar flux 1/27th of Earth's) from about 72m^2 of solar panels, weighing 340kg. So if similarly scaled 5W at Neptune is about 110kg + 24m^2 of solar panel.

And that's assuming that 5W suffices: "New Horizons" has 200W and a 2 metre diameter radio dish, and still took 15 months to download the data from its brief Pluto encounter (although at a slightly greater distance than Neptune's orbit)

If you want it to be an orbiter rather than a brief flyby then it needs some way to shed a lot of velocity: either a lengthy rocket burn and/or aerobraking by grazing Neptune's atmosphere.

So unfortunately it seems well beyond cubesat terrain: even a "cheap" probe to the outer planets is a large and complex machine.

You'd probably need a nuclear generator to power the thing.

AFAIK solar sails aren't able to slow down, so you'd need another form of propulsion to establish orbit.