I believe Bitcoin can survive for long time without any other alternate cryptocurrencies. It happened and that is the reason we are here with these much amount of cryptocurrencies in the marketplace.
If there is no Bitcoin these things might not happened and we need to think in that way only.
Then we people need to check out the volume and circulation of other coins with Bitcoins to compare yourself.
Why do you think that? Why can't Bitcoin live without altcoins? When bitcoin appeared, there wasn't any altcoin. This should not be overlooked.
I think Bitcoin can survive alone. But I can't say the same thing about altcoins. If Bitcoin doesn't survive, make sure there's no altcoin left.