Why can't Bitcoin switch over to Gridcoin's proof of work system? Gridcoin advertises itself as a "a mandatory competitive reward mechanism based on contributing the most towards BOINC projects on top of existing cryptocurrency technology."

Is there a reason why Bitcoin couldn't use Gridcoin's proof of work system, either to secure the system, or to distribute coins? What consequences would switching to their system have?

Related: What sort of calculations do the miners have your computer do?
Such a switch will never happen. There are three main reasons for this.


It would require the worst kind of hard fork, one where a lot of legacy code would have to remain in the coin, for the sake of validating transactions before the hard fork date.
While the reward system itself has been specifically designed to not be game-able (https://github.com/TheCharlatan/Gridcoin-Research/tree/master/contrib/BoincMonteCarlo), it is nevertheless destroyable by a malicious actor with reasonable funding, since it relies on a centralized service to distribute its data. 
There is little to no research towards the specific crypto algorithms used to secure user information in the chain, such as https://github.com/TheCharlatan/Gridcoin-Research/blob/CPID-style/src/cpid.h . In fact the CPID (which is used to identify researchers) is an md-5 hash of some string and the user email, so it definitely does not compare to Bitcoin's standard of security.