Unfortunately I have come to the conclusion that Roshone was necessary for the survival of the world and must, much to my chagrin, say that he needed to not be put in jail. Yes I will be explaining why, in great detail, with spoilers for literally everything. I do think Moash was absolutely justified in killing his ass though.
Without Roshone, Tien would never have been sent into the army, meaning Kaladin would not have enlisted with him. This leads to many, MANY problems.
1.) Tien was bonding a Cryptic. The reason Kaladin wasn't killed by Nale is that, for most of the time he was first bonding Syl, he had no Stormlight. For the time after that, there was only a single time anyone outside of Bridge Four took note of him doing anything strange (surviving the Highstorm). By the time he was known by the general population to be out of the ordinary, the Radiants were being reestablished and Surgebinding was legal. Tien would have been a Lightweaver in a position where extraordinary behavior on his part would be talked about extensively and a location where that gossip would get back to Nale. Even if he wasn't forced into the army, Tien would still be dead.
2.) Had Kaladin been sent to Kharbranth to pursue an education, one of two things would have happened. Either he would have joined the Diagram and thus become part of a cult that was literally sacrificing sick people to the Unmade, or he would have been sent home around the beginning of his residency without the money Lirin had stolen to pay for his education. Either his family (-Tien who would be dead) would be extremely poor or they would be middle class on pure, unadulterated blood money.
3.) Helaran Davar would probably still be alive. Amaram would probably be dead. Yay!
4.) Without Kaladin, all of Bridge Four would be dead, save maybe Sigzil (possibly being rescued by Hoid).
5.) Without Kaladin AND Bridge Four, Dalinar and Adolin would have been killed in the Battle of the Tower, losing two full sets of Shards. Renarin would be Highprince.
6.) Without Dalinar, Navani would likely either be assassinated by the Sadeases, assassinated by Szeth, or returned to Alethkar and killed by Aesudan.
7.) As Highprince, Renarin would likely either be assassinated by the Sadeases or Szeth, inducted into the Sons of Honor (somehow the good option), or discovered as a Radiant by Nale since his behavior would be more heavily scrutinized and thus assassinated.
8.) Shallan, no longer betrothed to Adolin, would likely have stayed with Jasnah or gone home to be executed with her brothers. All of her brothers would have been executed either way.
9.) Jasnah would probably have discovered Urithiru, IF it was still possible for her to get to Narak. However, without the visions from the Stormfather, I don't think she could have formed the Coalition.
10.) Even in Urithiru, without Kaladin and Bridge Four, the WIndrunners wouldn't have been reestablished to such an extent.
11.) No Dalinar means no Perpendicularity, all battles involving Radiants are done with limited Stormlight.
12.) No Navani means either Dabbid or Rlain MAY become the SIbling's Bondsmith, but more likely Urithiru falls to the occupation.
13.) Szeth would have never been defeated and thus would still be working for Taravangian, and he wouldn't have NIghtblood. Best case Scenario, Nale finds a way to kill Rayse with Nightblood. Worst case scenario...
14.) Rayse wins the war, takes over everything, and the Cosmere is doomed.