I really hate that narrative. Teams have dozens and dozens and dozens of people working on these things practically around the clock. It's not like they suddenly woke up after the draft and were like... wait, we might need to improve the club in the next two weeks?
OMG GET ON IT! Is the rotation good? Who's on the injury list? Do we need a reliever? Wait, who's in left field? What about the bench, how's that looking?
There's been talks going on for weeks guaranteed, its just the urgency picks up a bit and there will finally be some back and forth negotiation happening now.