The only reason an agreement protocol is needed is because nodes are allowed to have different opinions (in Bitcoin's case, on the contents of the block chain) and so the protocol agrees on one of these opinions. If a system could be designed such that there is no room for opinion then it would be obvious whether a block is correct or not and thus having more resources would not benefit an attacker. This might require too much synchronization to be practical, though.
The only reason an agreement protocol is needed is because nodes are allowed to have different opinions (in Bitcoin's case, on the contents of the block chain) and so the protocol agrees on one of these opinions. If a system could be designed such that there is no room for opinion then it would be obvious whether a block is correct or not and thus having more resources would not benefit an attacker. This might require too much synchronization to be practical, though.