The question contains a brief description of Bitcoin’s history, followed by this:
This description of bitcoin's history makes it sound like an awful like a normal commodity such as crude oil …. The net result (according to Hubbert, at least) is that there is a peak in the extraction rate of the commodity. This is often referred to as "peak oil" in the case of crude oil.
So let us go through it and see if Bitcoin really is like a “normal” (physical) commodity.
[Bitcoin] My (limited) understanding of bitcoin and other cryptocurrencies is that the costs of "mining" bitcoins was quite low in the early days
[crude oil] it's easy to get the first barrels out of the ground
Correct on both counts, but for different reasons. These reasons are discussed below.
In fact, in the early days of Bitcoin, the mining cost was so low that Bitcoin Core had a user-friendly “Generate Coins” option.
[Bitcoin] the limiting factor in how fast they were mined was the small number of people who had the infrastructure to do so
[crude oil] it's easy to get the first barrels out of the ground, when there's not much capacity to do so
Incorrect on both counts:
- Bitcoin: As explained in the other answers, the target rate of Bitcoin mining is arbitrarily set at one block per 10 minutes. To achieve this, the difficulty of mining a block is adjusted every 2 016 blocks (about 2 weeks).
- Crude oil: The initial ease of extracting crude oil was related to the large reserves of crude oil in easily accessible locations. The lack of activity in this area was only indirectly related; this lack of activity meant that the easily extracted reserves had not yet been extracted.
[Bitcoin] As time went on, however, the algorithms for mining bitcoins made it harder and and harder to get a new bitcoin
[crude oil] but it gets harder as time goes on
Correct on both counts, but again for different reasons.
Bitcoin Core’s “Generate Coins” option did not last long. The option was removed in 2011 via pull request #142, which noted:
GUI users … are unlikely to understand upon first contact that they will waste electricity for year(s), before possibly generating a single block.
The underlying code was removed in 2016.
Why was this? Of course, as time went on, the miners collectively became better at mining, and therefore mined blocks faster than the target of one per 10 minutes, which resulted in the difficulty increasing. As the difficulty increased, new ways of mining had to be developed. Mining moved from CPUs to GPUs to even more specialised hardware. (Interestingly, miners also began chasing cheap electricity.)
As for crude oil, producers naturally extract the easiest reserves first, meaning that the remaining reserves are more difficult to extract.
[Bitcoin] As time went on, however, the algorithms for mining bitcoins made it harder and and harder to get a new bitcoin in this way
[Bitcoin] and it is now rather difficult for anyone but the most serious miners to successfully mine a new coin.
Correct. Bitcoin mining now requires specialised equipment that is generally expensive to obtain and expensive to run. The difficulty of locating, never mind extracting, crude oil has also greatly increased.
Has anyone done a similar analysis to find out when "peak Bitcoin" or "peak Etherium" or what-have-you will occur? In other words, in what year will the rate at which new bitcoins are being mined reach its peak? Has this happened already? Or is there something about cryptocurrencies that make them immune to these sorts of effects?
We can now see that these questions do not make sense, at least not in the way you thought they did. In fact, there is another problem with your analogy: Bitcoin includes arbitrary reductions in the block subsidy (the amount of new Bitcoin created each time a block is mined). This has no analogue in physical commodities.
But, in practice, we can observe when peak Bitcoin occurred, which has been covered in the other answers. It occurred during the early days of Bitcoin, when the block subsidy was at its highest and an explosion in mining capacity overwhelmed the fortnightly difficulty adjustment.