webarchive.org is free.
The cost of putting data on the internet and having it stored forever is nearly zero.
The Internet Archive at archive.org, while free to use for individuals, has a yearly budget of USD$10m. The cost of storage media is quite cheap, but the cost of managing it reliably in the face of errors, accidents, and the changes brought by time can be quite high.
archive.org benefits from foundation funding, and the fact that its founder, Brewster Kahle, sold Alexa Internet to Amazon for USD$250m in stock in 1996, and from all appearances is trying to do a seriously important thing for the world.
And yes, they accept bitcoin:
"Can I donate BitCoins?
Yes, please do. Our BitCoin address is: 17gN64BPHtxi4mEM3qWrxdwhieUvRq8R2r . Every bit helps."
But don't trust randomly-pasted bitcoin addresses, because I might have just pasted my own there. Instead, visit their donation page yourself: https://archive.org/donate/index.php