Why did the rebels need the Death Star plans?

There were two parts to the Rebels destruction of the Death Star. The first was the knowledge that the reactor was unstable, that any explosion there could cause a chain reaction. That was the easy part.

The second part was that there was a tiny vulnerability, a way to get ordnance down into the core to trigger that explosion. To find that vulnerability, the Rebels needed the plans.

Without the plans, they would have had no way to exploit the weakness Galen revealed. Without the weakness, they'd have had no idea what target to look for in the plans.

He did not have the technical details to give or else he would have. He was working as an administrator of a kyber crystal refining operation. He worked on the reactor design and was able to create the thermal exhaust port weakness, but that does not imply that he had access to the final architectural schematics. In fact, it is pretty clear he didn't as if the plans were available anywhere easier to get to than Scarif he would have said that. So when he submitted his part of the designs the vent was probably just a line drawn on a circle. So he knows the vent exists, but without the final plans he does not know the coordinates of the vent on the Death Star. Even if he had a general idea from, say, seeing the designs in a meeting, that would probably not be good enough for the sort of fast precision strike needed.

According to the official novelization by Alexander Freed, he didn't know how to get the explosion to the reactor, only that it needs to be exploded:

Galen snapped back into focus, no longer hesitant or soft. “Saw, the reactor system, that’s the key. That’s the place I’ve laid my trap. It’s unstable, so one blast to any part of it will destroy the entire station.”
...
“You’ll need the plans, the structural plans, to find your way, but they exist. Sabotage from the inside is impossible: Krennic is too paranoid. But I’ve thought about this, Saw, prepared everything for you I could.”

And he clearly didn't have access to engineering plans to the whole station himself, being just in charge of the weapon. He knew where plans existed but didn't have access himself (else, he'd have said Eadu has them too, or as you said, would have sent them with the pilot):

...
“I know there’s at least one complete engineering archive in the data vault at the Citadel Tower on Scarif. Use what I’ve told you, run the analysis, and you’ll be able to plan your attack. Any pressurized explosion to the reactor module will set off a chain reaction that will-”
(Chapter 6)