The most important effects of the manner of Han Solo's death are upon Kylo Ren, and therefrom his relationship with and usefulness to Snoke. I think that the events of the film, from Snoke's point of view, were all leading to that moment.
Ren was seen to be struggling with 'the pull of the light' early in the film, asking Vader's helmet to 'show him the power of the dark side again.'
Note: Ren is dicussing his internal struggle with his Grandad's helmet and not Snoke himself. Would it be fair to guess then that finding the helmet, rather than meeting Snoke, was the start of his descent? Perhaps his loyalty to Snoke was not yet all it could have been?
Anyway, I digress... Leia also held out hope that Ren could be returned home by Solo - this would partly be based on her force sensitivity towards Ren. We saw her sense the death of Solo, but perhaps this was actually her sense that Ben Solo had finally lost his internal battle with Kylo Ren, and an intuition of how this must have come about.
The death of Solo then cements Ren's fall to the dark side in the same way that Anakin's belief that he had killed Padme and his child cemented his transition to Vader, and his loyalty to Palpatine. These are essential moments in the creation of the dark characters. Is it fair to say that these moments tend to be planned by the Dark Master, not happenstance?
We hear Snoke telling Hux to bring Ren to him after Solo dies, as he is now finally ready to complete his training.
The weakest parts of this film are that Snoke doesn't seem very irked with Hux that he has let his shiny weapon get blown up; that Phasma totally capitulates and takes the shields down with a gun to her head; and that the vital part of the weapon is on the surface, in a position that a bloke who has previously worked cleaning the toilets knows how and where to attack.
This bloke being pretty much the first ever Storm Trooper to go AWOL... conveniently having knowledge of how to destroy the big weapon, and how to get onto the planet...
The only bloke with the balls to fly a ship at light speed and land on the planet beneath the shields? Han Solo!
Imagine for a moment that these are not weaknesses of what is otherwise a very tight film; but clues as to the plan Snoke put in place to deliver him a fully fallen, guilt and anger driven Kylo Ren. From the escape of Finn to the death of Solo, all meticulpusly planned to deliver a Ren who is ready to give his full loyalty to Snoke in exchange for the completion if his training....
Imagine also that Snoke never actually wanted to find Luke. Luke will smell you coming after all. Snoke needed to draw Luke out. There has to be a rebellion to do that. Destroying it with a big gun would screw that up a touch.
So the plan was not to destrot the Rebels but to draw them on. Worked out pretty well!
Phasma is therefore completely redeemed of her apparent cowardice, by the way. Just following orders, guv.
Lastly, for me, Snoke has to be Plagius. How could a previously unsensed Sith Lord (you know he is) have arisen in thirty years, with nobody to teach him, if he was not already there before Palpatine? How could this therefore assumedly extant Sith Lord go unsensed if he was not hiding between life and death waiting for his time, in a way only he knew of? And how would this final series be tying up the whole nine films if it was not about finishing the cycle that started before the first one?