Even if you can successfully prevent that knowledge for 8 minutes, someone can still start working on some randomly chosen block and have hope it will give some boost on average, where other miners will be idle. Also, you need at least two candidates, in other case any obfuscation of the winner is pointless. Does it mean that nobody can start the chain alone by using the official miner?

Another thing is getting the right to mine: one miner can pretend to be N miners or can just own many mining machines and assign different keys to each of them. Then, if the list of participants is known, any miner can try to extend any block, just by checking each of them sequentially, or even assigning different threads to different blocks. Extending one of N blocks has the same probability as extending some chosen block. Because having a chance to mine the right block is better than having no chances by being idle, people will run their machines all the time.