For me its not a question of whether Jesse 'deserves' to start, its will his inclusion make a difference?
In certain games against particular opposition the answer would be yes, Jesse's running off the ball has for me been one of his best assets, it distracts/disrupts the opposition defending and allows space for others to exploit, but this 'off the ball' activity only worked when Jesse himself is deemed by the opposition to pose a threat if he does break late into the box, or bends his run to keep onside, or finds space between the lines and can receive the ball and finish.
In the last season or two this 'posing' a threat by Jesse diminished considerable (clearly some off the field problems were involved also) and whilst he still made runs, when the ball did arrive at his feet he was less than effective, hence his running off the ball became less of a threat. Jesse's spell at West Ham allowed him to find his 'mojo' again and needless to say raise his 'playing capital' once again. I suspect though that had he stayed at West Ham he would have attracted a lot more attention from the opposition, this season, than he did last.
The guy loves United and wants to stay, but its a 'bit part' generally and only for a specific purposes. IMO Jesse is not blocking anyone's path because he will not have a regular place, as much as anything because the way Ole wants us to play mitigates against some of Jesse's' skill-set, in a team adopting the style of pass and move, then alongside players like Mata, DVB, etc. he would have a better chance.
However we know he is not in the same class as Pogba, Bruno, Greenwood, Cavani, Sancho and of course now CR, so he is not expected to win the game with one piece of personal magic and until Ole changes our style of play to suit his skills set, then the best he can hope for is a run out in selected games, or for the last 20 minutes against a nine man defence who is tiring rapidly.