Drain the exchanges?

Have to remove circulating supply faster than miners are adding to circulating supply. They're always selling a certain amount of Bitcoin to pay their fiat bills.

The halving doesn't affect this. It doesn't cut their electric bills in half.

The fiat price going up or down is what changes the quantity that they must sell to pay the bills.

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Erm... Higher fiat price means more mining and more bills to pay.

Question: When Bitcoin is no longer priced in fiat, and 1 btc = 1 btc, what’s to keep the cost of electricity, and by extension Bitcoin transactions, from inflating beyond the reach of the average Bitcoiner

You're almost asking the right question. We will get priced out long before that happens actually.

If the wealthy, banks/corporations, and nation states start using Bitcoin to a significant degree, moving millions (USD equivalent) around, will they care about 'high' fees?

0.1% of $1,000,000 is $1,000. That will seem cheap to anyone trying to send over $1 million worth of sats, but will make it too costly for us plebs to use the network. Most of our UTXOs will become unspendable unless they've already been committed to lightning channels.

We'll be forced to use custodial lightning services that can afford to manage large payment channels for us. Banking system 2.0 for the poor. Financial self-sovereignty only for the wealthy.