I don't think the fees are going to "kill" bitcoin. But in the long run, making bitcoin less used as of today, yes for sure
The problem with high fees is that eventually the fees can be so high that the amount of bitcoin that you have in your wallet is enough to pay for the transaction in itself, this is happening with faucets but it may happen also to all of those that make microtransactions in bitcoin.
in fact transaction fee is creating problems as most of the people are not happy with the increasing transaction fee, i think this problem must be solve as soon as possible. because it is really effecting the image of bitcoin.