1) Death isn't his primary goal.
Palpatine is a master manipulator and we shouldn't take every word he speaks as gospel. It may seem that he's eager for Rey to kill him but I don't think he really is and it certainly isn't his primary goal. His preferred course of action is the one he's executing when Rey shows up: raising his fleet and reassuming direct control of the galaxy.
When Kylo Ren fails to kill Rey and she shows up on Exegol unannounced, Palpatine moves to a "Plan B" - his best option given his weakened state - where he solidifies Rey's turn to the dark side by convincing her to strike him down in anger/hatred/revenge.
Having died once before, he's not afraid of doing it again as long as the Sith lives on, his name lives on, and his spirit lives on.
Also, it's hard to even say for certain he'd let Rey kill him if she tried. He gave a similar pitch to Luke in ROTJ in an attempt to turn him to the dark side knowing full well that Vader would step in and protect him. The point was getting Luke angry enough to strike him down and it could be his goal here too. While my gut tells me he was willing to die, it's entirely plausible he had a contingency plan if Rey had actually swung her saber.
His idea of a best case scenario is further hammered home when - once he realizes
Rey and Ren are a Dyad in the Force -
he sees an opportunity to fully restore his power and takes it. That way, he can resume his original plan of raising his fleet. His attempt to kill her here and his earlier attempt to send Kylo Ren to kill her are both incompatible with the idea that Rey's turn is his ultimate goal.
I think it's pretty clear that she was nothing more than a "Plan B".
2) Snoke and Ren are means to an end.
If his ultimate plan is his own return to power, it makes sense to involve others. While his body is being regenerated, Palpatine is vulnerable and he knows it. Using other powerful force users like Snoke and Kylo Ren to execute his will is a lot better than exposing himself directly. By operating in the shadows while his body is reconstructed, he's able to keep the attention off of him and on disposable pawns that can be replaced if defeated without affecting the assembly of his Final Order fleet.