I think Bitcoin should manage the entire crypto currency market. First of all, it is already well-established in its properties cryptocurrency, leading in the crypto currency market. If there is no leader in the market, there will be no management, there will be chaos.
There is always going to be one coin that is the leader of the market, this is true not only in cryptocurrencies but in all markets as well, just look for the US dollar as an example of a coin that is the leader of the market and if for some reason it stopped being the leader then another currency will take its place, and while many have speculated that another coin could take the place of bitcoin that is not realistic at the moment.
To begin with the market cap of bitcoin is huge and it is the only coin big enough to perform that role and second the remaining candidates like ETH and XRP have several fatal flaws that will never allow either one of those coins to ever take the lead of the market.