Let’s talk about the transition into a PoS consensus algorithm and how it affects the value of ETH

So I know that there will be a gradual transition into the proof of stake algorithm. It will become harder and harder to mine blocks and we will reach a point where it isn't profitable to mine anymore and an "Ethereum Ice Age" will occur. My question is what will happen to us hodlers? By the economic nature of scarcity, wouldn't the ETH coin become more and more valued as it becomes more scarce? On the other hand, would it lose value because there are less miners, if any, to run the platform?