The price of a coin will go up but it won’t necessarily stimulate more expenditure of ‘mining’ energy because there are no more coins to ‘mine’. At that point

The price of a coin will go up but it won’t necessarily stimulate more expenditure of ‘mining’ energy because there are no more coins to ‘mine’. At that point the activity of miners would be better described as ‘transaction processors’ and in this phase, energy expended will be directly correlated with transaction fees. Yes you could say coin higher value would make the transaction fees ‘worth more’ but this effect will be completely dominated by the volume of the transactions themselves which will be much more variable. It’s like saying Western Union’s server costs can be affected by the USD/GBP exchange price. Sure, they can be but the far more dominant effect will be transaction volume.