Why DARPA wants blockchain based secure messaging system
As I see it, the key part is at the very end: "traceable in a decentralized ledger".  That feature isn't described in the EFF page you cite, and I'm not aware that any of the services listed provide it.

To see why this is important, imagine a scenario like the following:

Major Smith receives a message at 0400 hours from Battalion HQ about impending enemy action.  But he's too busy playing Angry Birds and doesn't bother to pass it along to his units in the field.  The enemy attacks at 1100 hours, the field units are unprepared, and they are defeated with heavy casualties.  Major Smith is afraid he will be court-martialed for failing to share the intelligence with his troops.  So he writes a message, backdated to 0500 hours, addressed to Captain Jones and ordering him to contact the field units and give them the information.  He also secretly orders (or bribes) Corporal Johnson, an IT administrator, to alter the message system's logs to show his forged message as having been sent at the appropriate time.  This way, he can blame Captain Jones for failing to act on the message, or at a minimum, plausibly claim there must have been some sort of communication failure that kept Jones from receiving it.

If there is a secure decentralized ledger of all messages sent, then Smith can't insert his fake backdated message in it, and there's no single person he can bribe in order to get it done.  So he can't dodge responsibility for shirking his duty.

A secure decentralized ledger is precisely what a blockchain provides.