Reading between the lines and guessing a bit I get the feeling Leesley was one of the bigger earners on the wage bill and Culverhouse had to get him out to free up funds to get other players in. He was getting in the team first few weeks under Cully until the week before when he'd likely already arranged to go, so may be not purely a footballing decision.
Joe Leesley has a podcast, there was an episode a couple of months ago with him and Jordan Burrow which was quite interesting. I think Leesley said something along the lines of 'he was told he had to go' when talking about leaving Boston implying it wasn't him wanting to go. Also noted about the Boston fans not liking him (can't remember exactly what he said will have to re-listen to it) which was a bit of shame, as I think he was generally appreciated just a few moments where a minority were on his back. Jordan Burrow generally spoke well of the club, resigning him when injured last summer and paying half of his private medical costs for injury. One of the things discussed was the difference between full time and part time, with generally clubs helping with rehab for injures more at full time and it generally being easier rather than juggling part time with another job, Burrow said he would be open to going full time again if he got the opportunity so I should think he will stay with our move towards full time ish next season.