How would that be any better continuity? Nowhere was it said where they were beamed from in A New Hope, it was vague. Vader simply said "Several transmissions were beamed to this ship by rebel spies."
Because the film makes it abundantly clear that they weren't "beamed" to the Tantive IV at all. They were hand-delivered.
As Pablo Hidalgo confirmed to me when I asked on twitter, after Vader did the walk of death on the rebels and the Tantive IV got away, the Imperials found No plans on Raddus's ship. So he had every reason to assume Leia's ship had them. Pablo said Vader did not see them passing the small data disc thru the door, he had troops between him and the guy at the door and wasn't getting the close ups shots of the disc everyone who was watching the movie got. If he saw the disc and thought it was the plans he would have force pulled it to him like he did their blasters. The novel implied Vader saw something but when canon is in question it is said to refer to the movie. Otherwise Yoda is blue and Jabba is humanoid. (Going by ANH and ESB novels)
I...don't actually care what
post hoc tapdance routine Pablo wants to put out. I mean, that's his job, and he does it well, but I find that answer wholly unsatisfactory to the events as depicted. "Oh, eh thought that because he didn't see it clearly." Well, isn't that
conveeeeeeeeenient. Because what
I saw was Vader walking down a hall, chasing a dude who had the tape in his hand, who then handed it through a door, got killed, and the Tantive IV took off. Which, to me, sure looks a lot like "hand delivery, not beaming."
Plus, I find it silly that Leia would try to bluff Vader when he was literally feet away from getting onto her ship. That'd be like guys robbing a bank, hopping in their car, the cops pursuing them, and when they pull them over, the guys say "What are you pulling me over for? I'm a member of the Imperial Senate on a diplomatic mission to Alderaan!"
I get why they did it within the film just on its own, I just think it doesn't fit as neatly as it should within the continuity of the film that immediately follows.
I think it would've made more sense to have Vader pursue some other ship out of system, which then beams the transmission to Leia's ship, which at least gives her SOME plausible deniability when Vader finally captures the ship and she acts as if she has no idea why the ship was fired upon. With Rogue One, her denial is patently absurd. Hidalgo's explanation kinda-sorta "from a certain point of view nudge nudge wink wink" makes sense on the "beamed" thing, but it sure doesn't explain Leia's behavior.
But that's ok. I'm well versed in establishing "head canon" and in my "head canon," the heroes of Scarif died on the planet, a message was beamed out to another ship, which managed to jump out of system, Vader pursued that ship, caught it just after it had
finished the transfer, spotted the only other ship in system (that being the Tantive IV), pursued THAT one to above Tatooine, and captured it. That, I find, makes both his statement and Leia's defiance make more sense.
The only reason they didn't do that in the film is (1) pacing concerns and why would you care about some random ship escaping and being chased by Vader's ship, and (2) putting the main heroes in that ship only to blow it up required them to really twist the story in knots just to keep them alive.
So, cinematically, there isn't a great way to get you to that point, even if that's really the best way for the longer-term narrative to make sense. Pablo can offer whatever explanations he wants, but at the end of the day, the answer is "Yeah, it's not the most elegant solution, but, eh, whatever. It's a pretty minor thing," which is probably what the production staff decided.
.
