Abstracting away from the corporation-specific concerns, there is an incentive problem. Vested interests can seek to lower the usefulness of the market's "price as a signal" by placing large diversionary bets. Granted, this is relatively less likely to be a problem in the archaeology space. What definitely may be an issue is lower liquidity.

Every time I see a post like this I think "where are all the prediction markets?" Regulations are one reason, but that's far from the only reason. If information/prediction markets are enhanced using new technology, regulators will begin to respect them more and allow for widespread use in non-academic contexts.