Your father sounds a lot like my grandpa, and I feel it's important that you stay focused on communication rather than diagnosis. This should help you identify and get past what's interfering in your relationship rather than attempting to fix his problem since ultimately he's the one that refuses to budge and he's the one that has to decide to loosen up.
When I talk with my grandpa, I remember that relationships depend upon long-term progress and even though he has a fading memory and health issues, he has a strong moral compass that helps him get back in the moment. At first, I offended him a lot because I pointed out a his hypocrisies such as how he believes in hard work but wasn't willing to focus on having conversations as much as he wanted to lecture me and how he is a goodwilling person but he wasn't willing to listen as well as talk. We would eat dinner or sit together in front of the TV, and I would ask him what's on his mind until he opened his mouth about whatever his feelings were. Eventually, the conversations would build up momentum since he became interested in whether I approved or disapproved of his patterns since I brought in alternative points of view in a non-critical fashion. This lead to him talking about the garden he tends to and the Italian-American club he joined and the restaurants in town he either loves or hates, etc.
My grandpa likes to talk about politics too since he reads the newspaper everyday and listens to the radio regularly, and because his positions are very stringent and elaborate I show him that I appreciate what he says by applying his opinions in contemporary context so he feels he's becoming more and more connected with the real world. I've also talked with other seniors who become closed off from this approach because they feel embarrassed and isolated, so I usually tell them to not worry about it and ask them if they want to play cards or look at a photo album instead. A lot of seniors are stonefaced in this regard because they feel their experience inherently carries wisdom along with it, but when they realize that their mind is missing something, they shut up. Some do it out of shame, others from confusion, others from sadness or fear or even relief since they're happy someone gets what they believe in even though they can't consciously explain that good faith to themselves.
If this happens, I think it would help if you bring up some of the old junk your dad has stashed around the house and ask him to look at it with you. He most likely doesn't remember or hasn't read through all the material, so take it as a joint reading experience; and if he backs away at first, don't despair right away. Try different publications and go easy since you might anger him if you press too hard.
I would also avoid the long-term goal of getting rid of all the clutter for now, but once your father opens up, you should tell him how there is a direct health hazard of the papers becoming moldy if they aren't packaged properly in order to protect them from humidity, how the abundance of junk is holding him back from enjoying himself in the community since he frets so much about arbitrary resources he hardly uses, and how his clinging to stuff dehumanizes himself from being social. If he's really worried about all the knowledge going to waste, tell him that he can donate all the publications to the local library which will gladly take them in order grow their reference stacks, and remind him that he can visit the library to read the material whenever he wants (which will give him the added bonuses of getting out of the house, getting some fresh air, and meeting new people, all of which should be principles he's an advocate of one way or another).
Good luck with your father. Just remember he isn't perfect and even though he might get emotional one day, that doesn't mean you don't have a shot and getting through to him later on.