4 reasons Jamie should travel to Claire’s time in Outlander (and 4 he shouldn’t)
Reason to go: Claire and Brianna would be safe
The 18th century is a dangerous place and Jamie knows that. When it came to Culloden, Jamie assumed he would die and sent Claire back to her own time. He knew that being with Frank was the safest thing for her and the baby.
One of the main reasons I could see him choosing to go to the future would be to keep Claire and Brianna (and then his grandchildren) safe. Outlander Season 4 will go into why Jamie being able to pass through the stones would have been a good idea.
Reason to stay: He knows the land
Being able to survive in the 18th century is a strength that many others don’t have. However, Claire and Brianna have adapted, because it’s easier to adapt to something you’ve read about than something you have no idea about. And they can go back through the stones if (and in some cases when) necessary. There’s no need for Jamie to take them to the future and get used to that world.
He knows the land around him. When it comes to hunting and the way of life he’s comfortable and happy. There’s a confidence to him that would likely be lost if he went to the future. It’s not worth messing that up.