That sounds like a good idea to me.

One of the tests for Fair Use in the US, as I understand it, would be whether the archived work "competes" with the original.

If people start going to IA instead to read the news, the newspaper might have a claim. But if they're doing it to get around paywalls, or purely for archival/historical/research purposes, that may be allowed.

But the reality is such decisions are subjective and will be up to whatever judge happens to get such a case in front of them if this is challenged.

In general judges seem to understand that the copyright holder has some interest in these situations but not seem to understand that the rest of the community has some rights too.