> Imagine any item with a certain amount of demand. Now cut the supply of that good in half. What happens to the price?

IMO the assumption/premise here doesn't describe the situation ("bitcoin" or more broadly "currency") in a precise enough way to make this a useful thought experiment.

Ordinary people don't really demand money per se. They work or sell goods/services and get paid money for that and they spend money to get other goods/services in return. There's no demand for money itself, it's just a means of exchange and value storage.
Now of course, everyone would like to have a little more of this "item", but that's not what demand is, really. Or would you also say there is demand for USD and if the FED doesn't meet this demand by issuing more USD then the price for USD increases? I'd say that's just deflation due to the supply of goods having increased (in a growing economy) in comparison to the currency.

> So you've got a dwindling supply flow, that causes higher prices, ...

Yep, prices are going to rise ... but as with most things in the observable world there'll likely be some kind of dynamic equilibrium. Let the price rise to 1M and combine that with the fact that even HODLers won't live forever (to wait for even higher prices) and you'll see many of them buy actual goods/services with their btc ... and what does that mean? Yep, there you have your supply and circulation of btc. People have real life needs and can't just wait for deflation to enable them to buy two new fridges in a year instead of one right now when the old one went silent.
Let the price rise to 10M and you'll see even more HODLers become buyers .. yes, there are some greedy HODLers out there (who probably prefer dreaming about what they can buy in the future over buying something now), but still, they will spend some and thus slow down the theoretically exponential price curve.

So no, I'm absolutely convinced that the price won't develop exponentially over the long term. Exponential price increase equates exponentially increased incentive to spend .. which is essentially direct negative feedback which leads to some sort of equilibrium.
And I strongly doubt that this simple mechanism is the only negative feedback mechanism for the price of bitcoin.

Yes, bitcoin as a currency would have a deflationary nature. Which should mean that it nudges people to postpone purchases a little bit into the future rather than spend as quickly as possible .. which to me sounds much more like reasonable economic behaviour (from a sustainability point of view) in light of the current planetary environmental situation, compared to a monetary system that incentivises putting money back into the economy as quickly as possible.

Ultimately, many aspects of society will probably function as a negative feedback loop for the price of bitcoin, since bitcoin isn't the only use for energy. It competes with other uses that are much closer to what people actually really need and can't do without. Like riding a train or using an electrical stove. People aren't going to stop riding trains because they could use the energy to mine bitcoin instead.

No, the exponential scheme would IMO only apply in some very limited economic model where all these real world negative feedback effects were left out.

Clearly, the outcome you describe (consuming 1/10 of the world's energy supply) is inacceptable. But since this outcome is based upon assumptions that (IMO) don't adequately reflect reality, it's not valuable for assessing whether bitcoin might be useful enough to legitimize its energy consumption.