If the subsidy varies according to past difficulty changes that would make it harder for miners to predict revenue and plan their investments.
I also don't think it is entirely accurate to say that supply is in-elastic. Production of bitcoins is constant but the number of bitcoins that miners are willing to sell can and does adjust according to price.
Mining is still profitable and that is why difficulty is rising again. The price will continue to decline for some time to come.
Bitcoin already includes some damping measures: eg difficulty retarget is capped at 4x up or 4x down.
This is another hypothetical damping measure, depending on the parameters. You could eg split the retargetting 50:50 (geometrically) between reward and difficulty.
As such that doesnt affect miners as the net-effect is the same: lets say difficulty was about to go up by the maximum 4x, then geometric mean is 2x difficulty and 1/2 supply. To a miner its net neutral if they get 6.25 coins at difficult 1 trillion vs vs 12.5 coins at difficulty 2 trillion. However it adjusts the supply reactive to rapid difficulty adjustments which damps price swings (volatility). And that is good for miners if miners like predictability.
As it is bitcoin mining is a kind of derivative on bitcoin price: its sort of slim-to-mildly profitable for the various efficiency operators, so there is a sort of keep the mine operating maintenance mode, and then if bitcoin price spikes by 2x and sustains, then it takes a three months for new equipment to be produced. Old equipment could be turned back on if the price change makes it break-even again, and longer term that could be a good thing for stability, but currently moore's law catchup is too fast so that old equipment becomes quite obsolete within a year perhaps.
(And bitcoin-mining with a few asics has so far is looking like a small loss making for me and probably many other hobby miners due to electrical cost and my lack of economies of scale).
Adam