i can't see efra allowing a one tyre policy for big events. There is massive competition between the tyre brands, and allowing only one brand would mean a drop in sales for the other brands a few months prior to an event, so a manufacturer who is not the event sanction provider would not like this.
Also as M7H said, the current system is open to people sabotaging others, ie passing a brush or a finger with additive or someones tyres, or dropping additive on a bench, or floor or god knows what to contaminate a racers tyres. We know people cheat because someone sabotaged Robert P's radio...so yeah, we have idiots out there prepared to do bad things.
it's probably cheaper for a privateer (as DSmotorsports said) to allow compound. I mean, what's the big deal? you put it on and race. it's $20 worth, as opposed to the headache of having to pre cut tyres hours in advance and spend extra cutting more tyres than needed so they can get tested (cutting 6 tyres instead of 4 sounds like a pain in the arse to me).
if compound was allowed then a racer can prep tyres in advance days or weeks prior if they so wish, or at the least bake the compound in at the track with tyre warmers.