Bitcoin's reward halves every 210,000 blocks, or about every 1458 days.

Imagine a century of a hyperbitcoinized world where each satoshi is worth $20 USD of today's money and assume mining is still required to secure the blockchain. The reward for mining a block is only from transaction fees, and everyone largely already operates on layer-2 or higher and the purpose of mining has transitioned to recording staking for opening and closing payment channels.

Let's compute the mining reward and subsequent energy expended to mine a block in this future. I use USD as a measure of energy.

Firstly, to compute the reward per block, you must consider wallet fragmentation. If we dont make a change to the protocol to address fragmentation, each sat might need to be a separate component of a transaction, and each component uses about 135 vbytes. If the block size is 1.5M, there is an effective limit of 11650 sats recorded per block (about $230,000USD at $20/sat).

If the maximum amount of total sats recorded each block is $230k, the tolerable fees would at most be %10, therefore the total reward per block is $23,000. This is small compared to today's mining reward (6.25BTC, or around $190k).

If the reward is cut by 8x, the total hash power applied will also reduce by 8x, and this assumes the market rate is 10% per transaction. If the rate is below 1%, the hash power will fall by nearly 100x which greatly reduces incentive compared to today.

This exercise shows the danger of leaving the wallet fragmentation problem alone in the long term. I can leave it to you to compute the rate of fragmentation and when this problem will need to be solved.

Without fragmentation, on-chain transactions will benefit from larger volume and likely miners will remain profitable and transactions remain economical.