I think part of the equation is how much is JBJ going to make on the open market once he hits free agency? Now, he's arbitration-eligible in 2019 and 2020, and becomes a free agent in 2021, so it's not like decisions need to be made NOW. But he's already making $6.1 million. He was a 2.2 fWAR player in 2017, and though he's gotten off to a slow start, his projected fWAR for 2018 is in the mid-2's. So he's well worth the $6.1 million. He could be one of those guys the Sox just keep for the next three years and then let go in free agency.
Or they could potentially move him. They have the highest payroll in baseball, and JBJ's salary (which will almost certainly go up in 2019 and 2020) may be one way to reduce it to allow them to make other moves. Moreover, his value also would interest other teams so he's probably got some good trade value.
I don't love the idea of Martinez in the OF full-time, so the Sox would have to replace Bradley somehow. The problem is that the Sox don't have any real minor league OF prospects to speak of. Their best minor league OF is....Rusney Castillo, but he'd cost them MORE than JBJ would so that would make no sense. And obviously Castillo, at 30, wouldn't be a long-term solution there anyway.
So to replace JBJ, the Sox, if they don't want Martinez as a full-time OF, would need to then acquire someone else. A veteran worth anything is going to be more expensive than JBJ so why bother? They could possibly acquire a nice prospect but that's really a future piece and how would they get said prospect? So the only real replacement they'd be likely to get would be a marginal player on the cheap. So that would be a pretty serious downgrade at an important position.
About the only thing I can think of is the Sox finding a contending team that has a quality OF prospect that's close to making the majors, but the team cannot afford to wait for that prospect because their time is NOW. So they see JBJ as someone they can immediately put into CF, improve their team now, and he can be their CF for the next 2.5 years at least. Then the Sox pull the trigger, send JBJ to this team for said prospect, and then either live with Martinez for the rest of the year, play the new kid they just acquired, or get a lesser, inexpensive veteran to plug the gap for the rest of the year before moving the prospect to the majors in 2019.
OR....maybe if they just decide they want to trade JBJ's defense for improved offense, a JBJ-for-Puig kind of deal could make sense for both teams. Their salaries and contract situations are very similar and maybe the Dodgers would value what JBJ brings (world-class defense and no drama) and the Sox would be willing to take on Puig to add his bat.
If Martinez was a better fielder, then yeah, trade JBJ and just plug Martinez into LF and Benny into CF. But that isn't something the Sox probably want to do. Dealing JBJ just isn't an easy thing.