None of them would have existed without bitcoin, but (don't crucify me for this) if bitcoin suddenly went away, other cryptocurrencies could fulfill the currency role that bitcoin had quite easily. And while those forked coins aren't popular on this forum, it's hard to argue that right now it'd be much easier to buy something with pretty much any coin other than bitcoin.
Let's understand the market psychology. If bitcoin vanish, no value at all. Value against the standard fiat unit goes zero then there will be panic everywhere. The myth will be everywhere that if Bitcoin disappears then another cryptocurrency form can disappear as well. Means everyone will move away from the entire industry. None will exist any more. Theoretically maybe one can prove it but practically vanishing all bitcoin node, vanishing all saved data of the node wonders is not going to happen unless the whole world suddenly goes back to the past when there were no digital form of technology, no digital data storage device.
Bitcoin is going nowhere, Internet is not going anywhere, crypto industry, crypto technology is going to evolve further.
Consider bitcoin as gold and platinum bar in physical form. Other alts are those of cheap silver coins. You can use these silver coins (cheap alts) for regular shopping.