Bitcoin is a currency and none of the currency depends on any other currency, but their strength is depended on its rate of adoption by the people and its regular circulation among the community. The more people accept it the more strength it adopt. So bitcoin is independent to altcoin or any othe crypto currency.
That is true that bitcoin is independent from altcoin and bitcoin alone I think can survive as long as there are supporters who used it. Bitcoin,the father of all crypo's is the standard in cryptocurrency.But an altcoin,from its name alternative coin, is really an alternative one.
Indeed, bitcoin could really stand alone without those alts as you said its the father of all crypto and altcoin are just dependent in to it, as you can see those altcoin could only be exchanged by bitcoin itself these means alts are just alternative , the name speaks for itself. Same as you said. Theres nothing to worry about if bitcoin would be the only one remains without altcoins,as long the adoption is there it wont die.
