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Document comments on Open Thread: April 2010, Part 2 - Less Wrong
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A straightforward counter-argument is that forgetting, i.e. erasing information, is a valuable habit to acquire; some "information" is of little value and we would burden our minds uselessly, perhaps to the point of paralysis, by hanging on to every trivial detail.
If that holds for an individual mind, it could perhaps hold for a society's collective records; perhaps not all of YouTube as it exists now needs to be preserved for an indefinite future, and a portion of it may be safely forgotten.
That's a good point, but rather than Youtube I'd suggest something like the exact down-to-the-molecule geography and internal structure of Mercury; or better yet, the output of a random number generator that you accidentally left running for a year.
For the record, the wording I came up with originally was "Storing information has an inherent cost in resources, and some information might be so meaningless that no matter how abundant those resources are (even if they seem to be unlimited), there will always be a better or more interesting use for them.".
(Edit 4/11: I was thinking of trying to come up with something like torture versus scrambling 3^^^3 bits of useless information, but that probably wouldn't be a good line of argument anyway.)