After my second playthrough i agree, the johnny silverhand storyline should be the climax of the story, it should literally be the third act of the game, maybe even the second act, but the first 10-15 hours of the game should be you building the rep required for anyone to think you should be stealing from yorinobu arasaka. Its actually insane when you think about it, that rookie V and Jackie even got the job in the first place. What Fixer worth their salt would give that job to two nobodies like them? There is an arguement to be made that dex chose you for that reason, that he planned on killing you on success or failure of the mission, but even still.
If you had good 10-20 hours of gameplay where you are doing the missions in the montage building a reputation, that story would make more sense and the events that unfolded afterwards would be much more impactful.
And whats great about this suggestion is, they could still do it, they could still add all of this to the game and retain the heart of the silverhand adventure that comes afterwards.