You must go beyond FLP impossibility. The problem with just stopping at understanding FLP is that it assumes too little about what is available. No assumptions of synchrony, no assumptions of clocks, then sure, consensus is impossible in the presence of faults. The real interesting question is, what realistic assumptions can I make to overcome FLP? I believe the CAP theorem is similar.

Also, if you're interested in cryptocurrencies or distributed systems with "greedy" participants, that's another class of problem that goes a level beyond byzantine consensus. The difference is that you cannot assume that even the "good" participants are running the officially sanctioned software, but rather you must assume that there may be colluders who attempt to game the network.

Byzantine generals problem + game theory -> ?