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.
both have similarities and sometimes the dynamics that occur between bitcoin and altcoins are not in line, for example:
(when the price of bitcoin goes up, the price of altcoins goes down) this is the dynamic that happens with both of them.
examples that are aligned between the two are: (when bitcoin goes up the price of altcoins also goes up).
From the example I mentioned above, I don't think the level of trust in altcoins will be lost, especially altcoins that already have many uses.