No, you don't have a legal right to a refund. The allowance isn't itemized separately, it's included in the ticket price. There is nothing to refund. It's also in the contract of carriage, to which you agreed when you bought the tickets.

So, while it's certainly a cute idea, you have no legal recourse to it.

Of course, many airlines have implemented your idea, just in reverse... they've removed the free bag allowance entirely, so if you check a bag, you have to pay for it. If you don't check a bag, you don't pay for it. So, you'd still not get any refund, you'd just not pay. Since many airlines have already reduced the free bag allowance even on international flights, your wish might just very well come true sooner rather than later... just not quite in the way you'd hoped.