Just to elaborate on my first point, that Jyn being the designer's father had no purpose to the story, and indeed made no sense, you could cut out the opening scenes and cut out the initial mission where Jyn's father was killed and not affect the story. The chief designer had no real purpose in any of it, other than having sabotaged the design. But that plot element undercuts the plot of Episode IV, that the rebels got the plans and found a flaw. So his character was completely unnecessary. His daughter was even more unnecessary because Jyn being the chief designer's daughter had absolutely nothing to do with what she did, other than the completely useless waste of time they spent on the raid where she saw him die - right before he was going to be executed anyway.
It didn't matter how the rebels found out there was a Death Star (which of course must have plans somewhere or the contractors wouldn't know what to build). In fact, it's pretty much impossible to keep a project that large a secret from the Senate that's paying for it. They didn't need any cryptic message from the project's chief designer. A cryptic message from any one of the 300,000 construction personnel over the 15-year period would have done just fine to set up the reason for a raid to steal the plans.
And of course the chief designer's "critical role" conflicts with episode III, where the trade federation showed a little hologram of the Death Star, a hologram they wouldn't have unless they already had the design pretty much done, at least to the level of knowing how all the key components were going to work. Once they had that, the rest of the design work is toilets, lights, and hatchways.
So instead of having an elite team of agents steal the plans in a brilliantly conceived and executed mission, the story sinks to having a random gaggle of poorly developed characters stealing them on a lark because the Rebel leaders wouldn't approve such a mission.
And of course stealing the plans wouldn't have been necessary if the chief designer had simply told the transport pilot how to destroy the Death Star by hitting it in an exhaust port at coordinate latitude X/longitude Y with a torpedo launched from a small fighter. Whew. That would avoid the need for the entire movie.
So if they went with the chief designer story, they didn't need the raid to steal the plans, and if they wanted to go with a raid to steal the plans, the story didn't need to include the chief designer.
And how did Lord Vader know the rebels stole plans? They might have been stealing the budget requests or internal audits or evidence that the Emperor was involved in a murder. The Imperials could have figured out exactly what the rebels stole from the data core - except that they blew the data core up with a blast from the Death Star before any investigators could take a look.
And on a final note, if it only takes a few seconds to transmit the plans from one computer to another, across orbital distances, why is anybody even searching for a data disk of some sort? Why didn't the rebels transmit the plans to all their ships and have everyone scatter, to transmit the plans to all sorts of different planets until nobody in the Empire could visit their favorite porn site without seeing "We have the Death Star plans! Click here to read!"?