Bitcoin IS the concept of cryptocurrency in itself, so if Bitcoin dies, so will all other altcoins and the whole idea of cryptocurrency.
This is only true if the reason Bitcoin dies being because of a reason that is applicable to all of the CryptoCoins. The main force here would be Government opposition.
However, it's not inconceivable to imagine a scenario where Bitcoin fails due to another coin winning over the market due to some feature that Bitcoin just does not have.
There is nothing that other coins can have that can't be implemented unto Bitcoin if the developers see it fit enough to do so.
I disagree, the Bitcoin core development team are careful, their product is responsible for billions of dollars in wealth. They are not going to implement features to compete with other coins in a timely manner.
To show an analogy, see Silicon valley and its startup culture. Quite often smaller, more nimble companies are able to fight and sometimes even ruin much larger, much better resourced companies.
Actually, come to think of it, developers aren't really relevant at all. What made Bitcoin the only one there is is because of its first mover advantage. That's just how deflationary products work, the earlier you are, the more valuable you become.
I urge caution here, Bitcoin is the first example of a real world deflationary product and it could/will face competition.
Remember that Bitcoin is two things, a store of wealth and a decentralised digital cash transfer network, if a much better system emerges that makes that storage safer, more private and also makes the transaction network more usable, you might find the first mover advantage is not enough.
Also the developers do matter, if the entire core team and Satoshi tomorrow said they are releasing Applecoin and dropping Bitcoin for various explained reasons, the market may react and follow.