So in a year or two when the returns of mining bitcoin reach zero,
I don't understand why you think that the returns of mining would ever reach zero? That isn't how mining works. Perhaps you need to learn a bit more about the process.
what's going keep bitcoin alive when there is absolutely no [monetary] incentive to compute the hashes?
If there were absolutely no financial incentive to mine, then mining would not succeed. Fortunately the protocol is designed specifically to maintain a financial incentive.
I'm sure the guy who made bitcoin has some fail safe in mind?
Yep.
The difficulty is adjusted to maintain a timeframe of approximately 10 minutes per block. So as people stop mining (due to it being unprofitable for them) mining becomes more profitable for the remaining miners (same number of coins per minute distributed among less miners). Eventually there is an equilibrium where only those miners who have the best equipment and lowest energy costs remain and they continue to mine profitably.
Depending on the good will of people to continue mining for no return simply isn't reliable enough for bitcoin to be a dependable and legitimate currency.
I agree. Fortunately bitcoin doesn't require any such dependency