My OBS recordings (of mostly game footage) come out to between 1 and 1.5 GiB/hour for 1080p resolution. Given that simple external HDDs start at about 20€ for 500 GiB, that comes out to 6 cents of storage per hour recorded. Your power bill for the gaming PC is going to be higher than that in some places.
I have only streamed for slightly over a year, so I cannot say anything definite about "years-old footage". But I can absolutely see myself going back to that footage when I get nostalgic about any of the games that I've played. Especially with games that you can only realistically play once, like Outer Wilds.