I can clearly see a path in which the Bitcoin already mined will be used to secure the blockchain in a future proof of stake dialect, in a not so distant future. If the chain - and I mean Bitcoin - will stop minting tokens at 21 million, the actual functionality of the said chain must be supported by the staking of pre-existing Bitcoin.

You may have a point. Suppose the price of BTC goes up by 100x in the coming decade. We'd be looking at BTC at $1.8 million. Because the cost of mining one Bitcoin follows its market price, mining Bitcoin at a price level in the millions of dollars could prove an environmental disaster. Suppose the average cost of mining one Bitcoin were $1 million in 2029. That's two mining reward halvings from now. The annual issuance rate of BTC will be 1.5625 BTC per ten minutes, which is equal to 624365 = 82,125 BTC per year, which would be worth maybe $82 billion. The energy cost of mining Bitcoin is between 90% and 95% of the total. Let's say $72 billion.

https://www.investopedia.com/news/do-bitcoin-mining-energy-costs-influence-its-price/

At the same growth rate, the total electricity generation market would be worth $2,095 billion.

At $1 million dollars per BTC, the share of Bitcoin mining of the world's electricity generation would be about 3.45%. It's not an overwhelming proportion but it is quite a lot.