The word "Alt-coin" should mean "Alternative Coins". And the word alternative in a layman's language should mean having an obvious option. Example, having an alternative plan means I can decide to use Plan B, most especially if plan A may not favour me at that time. Also, Coffee is an alternative to Tea, in this scenario, alternative is a choice and not a measure of importance. In a situation where an alternative is a choice, is therefore means that the Sorrow of one will be the pleasure of the alternative.
Relating this to cryptocurrency, if BTC who is the mother of Cryptocurrencies and who has gained extensive trust ceases to exist today, will altcoins flourish or will it make the people loose total interest in cryptocurrency.
This is an interesting question and in my opinion it will depend on the reason behind the supposed disappearance of bitcoin, if this happens because a flaw is found in the code and governments are able to destroy it or because there is a cataclysmic event so big that people need to go back to the Stone Age then there is no way for altcoins to take the place of bitcoin, however if this happens because a new coin is created that is many times better than bitcoin then it is obvious that alternative coins in that scenario will keep on existing and now are going to be based in this new superior coin.