Does anyone think Coca-Cola or any other big for-profit entity would want to align itself with a needy institution and thereby possibly damage its own brand?
Another thought: How about the entire field agree and put into practice an across-the-board rate, a percentage of all gifts and grants that would go toward indirect costs. If it was 25%, a donor of $100,000 for an exhibition would know upfront that $25,000 of the total would be allocated toward operations.
Maybe that hypothetical wasn't the best example... I like your idea about an automatic percentage of donations going to operations, but I wonder how that would affect the amounts people donate. Especially for donation packages built around the costs of specific projects or opportunities, would donors still want to give the same amount (and thus not fund the project to the desired degree) or would donors be willing to give extra to fulfill both the project's needs and operations allocation?