Villains shouldn't repeat the same mistakes. Often in fiction you'll find that they do, or that they repeat the mistakes of someone who went before them.
Let your villains learn from their mistakes, and the mistakes of others. If something went wrong last time, or the heroes exploited some weakness, have the villain correct the error, plug the hole in their plans, shore up the weakness to make certain it doesn't get used against them again.
It's only sensible. And we all know villains can be sensible, right?
Commentary by memnarch (who has not seen the movie)
Aha! Rey is a secret Jedi! Or... is going to be one in the future. If Luke actually gets found again seeing as the only other known Jedi died 30 years prior. And is fine with training someone come to bother him, even if they're family. And he also isn't dead already. Being a Force ghost might alleveate that somewhat, but Obi-Wan didn't seem like he was able to stick around much, which would make proper training difficult.
Technically that did work out well for Palpatine, it got Anakin to stop haunting him! Other than that, I'd thought this was a callback to Episode VI the movie (which wouldn't make any sense), but it turns out there was actually a scene that brought it up! That said, this feels a bit off as it's getting away from the Episode IV parallel of Rey needing training. Maybe that was intended to be an ongoing struggle across the movies instead of contained to a single movie like Luke had. I can see Disney wanting another movie series-spanning set-up like the MCU, even if it might be a little complicated for the immediate viewing audience.
I bet Kylo doesn't completely follow Snoke's instructions here for finding and killing Rey; it'd be much easier for Kylo to get back at Nute (or the movie-equivalent) by having Rey kill Snoke off, then killing Rey. After that, Kylo can stage a takeover of the First Order from this giant figurehead. This might not be a good plan to follow, but Kylo does like bad plans after all.
Commentary by Keybounce (who has not seen the movie)
So the idea was to compare this movie to Episodes II and V. We have "Locate the missing last Jedi and extinguish them". We have "Luke Skywalker must not complete his training / What if he could be turned?". And I love the answer: "Just find her and kill her". Yep, don't bother trying to turn your enemy, just get rid of them. So much smarter.
Now, contacting the agent in the Resistance? Well, with Poe "dead", apparently, our only remaining agent is Finn. The First Order trooper who did not fire because he realized that no one in that group could have killed his partner. The First Order trooper who started to wonder if the First Order really was the good side or not.
Finn wanted to do a straight up spy mission, instead of all this front-line action. He admired the "Second Reich" vibe, the "we maintain strict discipline". He wanted to feed intel back to the army.
In the #1880s, Finn and Poe escape. Finn seems to go from "This is just pretending" to "This is for real". My takeaway from that was more of "I really have become independent, and need to fit in". So if Phasma, Snoke, Hux, and Ren are going to reach out to him, what will he do? Well, chances are, he'll do good in either side, based on which one he likes better. So which one will he choose?
Let's see. One is is already on top, and he's high-ranked in that side. The other side is... really disorganized, barely holding itself together, full of deception and lies, and about to fall apart any second.
Yea, I know which one I'd put in with. The one that's the actual organized government.
Snoke: Amidala must be found. The crackling flame of the Jedi must be extinguished.
Snoke: And then silence, glorious silence, shall fall across the Galaxy.
Snoke: In particular, Rey Solo must not complete her training.
Kylo Ren: There is another solution. If I bring Rey to you, we could turn her to the Dark Side.
Snoke: Oh, capital idea! That worked out so well for Palpatine, didn’t it?
Snoke: Just find her and kill her!
Kylo Ren: The Black Alpha spy network is on high alert.
Snoke: Speaking of spies, contact that agent in the Resistance and clean up Hux’s mess.
General Hux: Hey!
General Hux: Hey!!