Price of Bitcoin is what drives the crypto market. I would say bitcoin is not heavily relied on altcoins like altcoins are dependent on bitcoin. Whenever we see bitcoin going up we see altcoins also going up but inverse is not true. There is no altcoin till date whose value has affected bitcoin in any way.
Its economy, there cant be just one currency, just one market. Beauty of crypto is connection between coins and tokens, and simplicity in making transactions, storing, and swapping coins/tokens. Its pointless to talk about can bitcoin survive alone or it cant, we cant deny existence of all other alts.
Bitcoin and other alts rise in price as demand rise and cash inflow. Bitcoin is the most favorite coin, and like that mostly people invest in trade with bitcoin, of course that bitcoin price will rise first, and when people finish with bitcoin they turn to alts, they always comes second.