If it's free, miners don't need to send the transaction fee back because senders would not even add transaction fee to the chain. Nothing to return. Is possible to send Bitcoin without fee? I'm not really sure, fee is like a fuel and every car needs fuel to be able to run. Not sure about zero fee but it's absolutely possible to make the transaction fee near zero, unfortunately there is always a fee war. Some people agree to pay more fee to accelerate their transactions or simply ruin the chains, make it very busy so other people will move to other coins. This is the problem, even though the fee is 1 Satoshi, I think we would never do that because our transactions will take forever to be confirmed.
yes you are right when the fees of transaction is very low then it will be more helpful and useful for lots of people to get the extra profit for their mining and the investment definitely a good chance to implement and the possibility of people to increase input field is also there.