I think it will survive until people believes in the technology. Since bitcoins can last indefinitely in theory, bitcoins will be relevant if there are people that are willing to buy and sell it. The 21,000,000 bitcoin cap is just the number of bitcoins that will go out in circulation. The part of mined block, is just actually rewards. Miners can still continue mining blocks even without rewards. I guess that's a good thing for us, since our transactions will still be written in the blockchain. But I don't think I'll live to see that day since it's so far away.
I strongly agree on your opinion that, it will survive until people believes in the technology and since bitcoins can last indefinitely in theory, bitcoins will be relevant if there are people that are willing to buy and sell it. And adding also my opinion that, bitcoin will technically survive forever, it is kept running by nodes all over the world. And it cannot just go down at some point unless there is a catastrophic world event like an asteroid or something of that nature. In addition, no one knows how long Bitcoin will survive! we can never tell and I think it depends on the users. As long as there are people that are willing to use it, Bitcoin will continue to survive.