Boxing, or using your hands with the threat of shooting and takedowns behind it is very different to actual boxing, with full-sized boxing gloves and nothing but your guile, cardio/output and heart to carry you. feinting, shifting your feet, doubling and tripling up your jab and so many other things barely exist in MMA, one because you don't need it to be lethal and two, because it's a real art form that takes many, many years to master. If you think about all the facets of MMA, only those who come from striking backgrounds are going to have even a fraction of the time worked on these skills for them to be instinctive and superfluous - most fighters revert to type and any surface level skills learned along the way get tossed to the wayside the moment things get out of hand, which is where you see wrestlers instinctively shoot for the legs when the striking gets too hot for them. Fighters like Usman, Covington and Cormier are an anomaly in that they keep striking even when things get out of hand, but Woodley is not.
He shells up, or tries to fire that bomb punch with little inbetween. Woodley doesn't like being hit, and he knows he has a terrible tank so he tries to conserve his energy, which he gets away with more in MMA than he will in a boxing ring where he needs to have a skillset and range in his hands (jabs, feints, crosses etc.) that he simply doesn't have. To hurt Paul, he has to open him up. Woodley doesn't open anyone up - he knocks them out with a bomb or two.
On top of that, if Woodley's going to throw at a volume that matches Paul, his power will diminish rapidly as he has no stamina.
I don't see what Woodley does to get inside a much longer man's jab - he has no head movement, and he doesn't move his feet well either... If you take the threat of his wrestling away, there's only the bomb right hand to concern, and you have to set that up to land it, which is where his level feints from wrestling are so much more of a threat in MMA and what makes that single bomb effective. It's not applicable in any way in a boxing ring.