You should be able to do that because you have paid for the right to do so - i.e. it is part of the contract.
Pay a high price for the ability to no-show and receive a refund, or choose to pay much lower for a fare which does not provide a refund.
It is the airline's responsibility to manage the consequences of the terms and conditions they offer. In the cases stated, of pax booking 3 or 4 refundable fares, then choosing the one they want, it is up to the airline to manage the pricing.
Let's say I can book a fully refundable (even after no-show) fare for $1,000, or a fare that cannot be refunded for $300. If I have a choice of 4 flights, and I will take one of them, I can either pay $1,200 for 4 non-refundable flights, no-show on 3 and lose those fares, and fly on which ever I want. Or I can fork out $4,000 for 4 refundable, fly on one, then later get $3,000 back. I get to fly on the one I want for $1,000 (at the price of having to have $3,000 with the airline for a while until I get it back - provided the airline doesn't go broke).
If the prices are changed, and the non-refundable is only $200, then it is cheaper to book and throw away.
Either scenario sees the airline with a certain amount of revenue - and 3 empty seats. The refundable fares would be more attractive for the airline, as they will be able to predict that a certain percentage of those will be no-show (after all, why would someone pay that much if they didn't need the flexibility - just buy the cheaper fare). The non-refundable fares are more difficult to reliably infer whether or not they are being used as throw away because it is cheaper.
In any event, I fail to see that removing fully refundable, even after no-show will really address anything.