Given the number of rebels they captured at the end of Rogue One who came straight from Yavin, why did Vader and Tarkin need to go to such lengths to extract that information from Leia? Just what happened to the rebel fleet after the end of Rogue One?
Keep in mind that the Empire doesn't know all these rebels came from the base on Yavin. For all the Empire knows, they could have come from all over the galaxy, meeting at a pre-arranged point for a large pre-planned mission, without ever knowing the location of the primary rebel base.
They go after Leia because time is a factor. Leia is a known public figure, which means a couple of things:
- as a high-ranking official in galactic society, and presumably in the rebellion, there's a better chance that she actually knows where the base is.
- they have leverage over her automatically - to wit, they know which planet she calls home.
If standard "interrogation" techniques don't yield fruit they can (and do) threaten her family. Indeed, the whole planet. This is a heavy-handed approach, but it's their best bet at finding the location they need quickly. And Leia is the highest profile captive they have, upon whom to use these tactics.
Sure, they could've done the same thing with each and every faceless rebel grunt they caught, but they would've had to spend time figuring out who these people are, where their homes and families are, etc, etc. They were probably smart enough not to carry (legitimate) identification tags on the mission, so this process is going to be more than just typing one name per captive into the Star Wars equivalent of Google Maps. Plus, they only have one Death Star, so they'd have to travel to each and every planet they found to pull the old "tell us or we'll blow up your home planet" stunt.
Even after all that, the rebels could lie. (Indeed, Leia does lie even though they have her dead to rights.) They could break under torture and just tell the Imperials whatever planet they seem to want to hear. Given how big a galaxy is, it could take years to run down all those leads and figure out which, if any, were legitimate. During that time, the rebels surely would have relocated their base of operations anyway.
That the Empire needs to question people at all and aren't trying to dig the information out of the ship's log or navicomputer says to me they've at least taken some basic precautions to protect it's location. In all likelihood, none of those soldiers actually knew the location. Sure, they may have been there, be able to describe a jungle moon orbiting a gas giant and the ancient ruins, but that could be one of thousands of obscure corners of the galaxy or some entirely uncharted world. If the rebellion had any sense the name "Yavin 4" would be kept classified and the co-ordinates kept only by high ranking members.
Captain Antillies may have known, but Vader killed him trying to get him to talk about the location of the plans (his immediate priority at the time), hence later: "now she is my only link."
This will probably get downvoted, but honest answer is they didn't need Leia to learn location of Rebel (base)s . Any decent military here on Earth is capable to process dozens of POWs at the same time. Ruthless galactic war machine like Empire would have lots of professional interrogators coupled with torture droids to extract information. Not every Rebel is strong-minded like Leia, some of them would certainly break more easily. In real life, any guerrilla movement must not stay in one place for too long. Rebels of course knew that, so they would relocate periodically (Dantooine->Yavin->Hoth) . Why they didn't leave Yavin earlier after Battle of Scariff is not entirely clear.
One thing to note, Imperials still needed Leia to get plans for Death Star, but whole plot of letting her escape to learn location of main Rebel base is now completely illogical, after Rouge One retcon.