The price of the supposed new top coin would determine the price of other cryptocurrencies in the coin market. This coin would have to have some extraordinary features aside blockchain. It's clear we haven't reached that stage yet.
It does not necessarily mean that would happen. The fact that bitcoin as the highest market cap does not mean the reason why its movement control the market. It simply because it is the first, it has a huge support, it is tagged as a pair with most altcoins and this makes it hard for a lot of altcoins to stand on their own. Market cap to me is really not the judge of a support for a coin as some coins like XRP or EOS which is centralized can even easily be manipulated to that extent.
Anything will happen. I think some people or investors will immediately select the new one. But let us not be afraid of losing, instead we must strive hard in order for us not to be eliminated.
But definitely I will not select. Marketcap is a least significant measurement for me to choose one coin for longer investment in my view. No one is calculating it based on circulating coins even they consider only circulating, devs themselves own more number of coins. Then why we should consider it as an important criteria ?