Mining isn’t used to validate transactions. You can validate transactions without mining. It’s purpose is to secure the network. The network validates transactions using asynchronous cryptography and nodes only transmit valid transactions. Mining secures those transactions from being overwritten.
It's possible to validate transactions with proof of work and compensate the work with transaction fees rather than the creation of new coins.
If your crypto-coin starts life with all the coins instantly sprung into existence, that means everybody gets to buy their coins from you--the founder. There is a name for this--it is a pre-mine scam. All you do is mine most of the coins yourself, then go pimp your coin so it gets some buyers, and sell them all off for a sweet profit.
But the amount of work required to validate a transaction need not be as much as it takes to create a coin, and people will continue to be willing to pay someone 5c to do 4c worth of computation to validate their transaction.
