Quite simply, the coin price indicates support. After the split, there will be two versions of the Bitcoin network with independent prices. A non zero price indicates non-zero support, and as long as it's at least 25% of the original price, it'll probably be okay.
A high price indicates high support.
In the long term, the hashrate follows the price. Miners will mine the coin with the highest price, because they can't afford any other option. Electricity is expensive.