You realize that if people do as you request in your last sentence and stop mining, transactions will stop and you won't be able to send your Bitcoins anywhere? The elegance of the solution to convincing people to process transactions is to reward them for doing so by mining. Satoshi created the incentive to produce the required behavior correctly; not enough people would have done the computational work necessary to really secure the blockchain without it. The fact that we now need ASICs to efficiently go through the mining process means that it is difficult and expensive for any one person/organization to do a 51% attack on the network.