There is no such thing a free money, this is what the fed attempts to do with quantitative easing and stimulus bills. There is only so much value in a network, if you increase the amount of money in a system without validating its existence, it decreases the value of all money proportionally.
But as I said, mining validates the need for new currency. Currency will only be given away when people are mining, and mining is not ever required to be happening like it is in bitcoin and its derivatives. Security of the network is completely separate from mining.
What you are suggesting is a tax on the network to the advantage of transactors in an attempt to further stimulate spending.
These inflationary measures will not doing anything but trickle-up, as we have seen in recent years. Creating a central-bank in protocol is opposite to the bitcoin design philosophy.
As we have seen? We have seen nothing but crony capitalism. The fed doesn't print money and helicopter it into the economy, it prints new money to bail out banks and serve congressional interests.
In addition to that, as I have stated, mining is required before free money will be created. One way or another, as the economy expands, value has to go somewhere. It either goes into existing currency by enriching only those who hold more than average amounts of the currency, or you can use it to enrich a much wider array of people. Including those who might be on the fence about accepting the currency.