I think that would get into murky water really quickly with the rights holders (/content creators) not exactly being thrilled the Wayback Machine is essentially monetizing their IP behind their back.

It wouldn't be behind their back, like I said, "Maybe let website owners decide which scrapers are allowed to use their content, or allow them to get paid for use of it."

Interesting, in all the years I have never noticed that IP has 2 meanings (well probably more...) Yeah, I am an engineer and usually try to avoid the legal BS. Although I hate that AI has made stealing legal if you are big enough.

If the money was guaranteed to only be used to pay the costs, there probably wouldn't be any problems

No. What happened to their remote library scheme? They did not make if for profit, but still...