If most of the Bitcoin Core clients, including all the "light" wallet servers like Electrum and Mycelium, and businesses (like Coinbase) switched over, then the

If most of the Bitcoin Core clients, including all the "light" wallet servers like Electrum and Mycelium, and businesses (like Coinbase) switched over, then the bitcoins created by the miners on the "old" blockchain will completely lose their value as they would not have any uses. They'd have no choice but to switch.