BTC will never be a stablecoin; it's impossible. One of the characteristics that sets it apart from any other market is that BTC will always be volatile. It moves a lot, with buying and selling everywhere. It's impossible; it would cease to be BTC and what it was created for.
I agree that volatililty is one of the things that comes with bitcoin and nothing can change that about Bitcoin. But I don't think that the OP's question is whether or not BTC will eventually become a stablecoin. I believe that the question is more like trying to know the mind of investors behind their reasons for holding Bitcoin, is it just for the profit or are there other reasons entirely.
Just assuming that the price of Bitcoin would be fixed forever, would people still appreciate the value of holding on to it for years or even to generations? I don't know about you but for me, I feel that's an interesting question for discussion because it take our mind away from the idea of price appreciation and focuses on the significance of Bitcoin as a long term investment.