It would be interesting if the Oilers tried him as a line driver for his own line and he succeeded. His price would go up even more than when playing with McDavid and getting points there. Obviously you could always trade him then, but I'm pretty sure other teams would try to attribute his points to McDrai and thus lower his value.
Not trying to put Pulju down, but is it really a good idea to give him responsibility to drive his own line right now? I mean, there's a good to fair chance that he's going to be the kind of player who can, at least at times, carry a scoring line. But so far it seems this set-up is working for Oilers and Jesse's confidence.
Playing alongside Drai and McDavid as the "responsible third wheel" is doing great things for him. He'll get his opportunities and goals/points and he has a chance to mature his offensive game more and more.
Although, ultimately I think Pulju (or whoever is going to be the third big F wheel in the Oilers long term) will need to be able to drive his own line. He doesn't have to be Drai/McDavid level offensive juggernaut, but chip in offensively and check out the opponents. Come playoff time it's a huge benefit. Rolling three efficient lines will grind out most of the opponents in 7 game series.