It is the cost of mining that adjusts to the coin price, not the other way round.
It is a common fallacy to believe that the price comes from the cost to produce something, it is called the labour theory of value, and it has been shown to be wrong. This is demonstrated clearly with bitcoin, which is a rather clean experiment, because it adjusts so quickly. The market finds the right price with someone offering to sell coins, other to buy coins, the hashing cost follows.
And also it is the cost of mining, not the hashrate, that is decided by the value of the coins.
With gold it is the same. Some people in the gold bug community understand this, and they can show that the production increases with the increasing market value of gold. It is not so clear, because the investment needed for gold production is so large, but if you compare price and production volume (in gold there is no difficulty adjustment, so produced volume will increase), you can see that there is a delay of about 10 years, understood to be 5 years to make the investment decision, then another 5 years to actually develop a new mine. The cost increases for the new mines because they use slightly less rich deposits, and the mines with better richness will increase their cost by more expensive land cost, more tax. higher labour prices and other cost driving factors. Likewise, the profit can change a lot but will slowly converge to the general profit level, which has its roots in the time preference. With this mechanism, nobody gets free gold, you have to buy it or mine it for approximately the same cost. As in bitcoin, anybody can mine, and gold is everywhere, it is in the ground you stand on right now, not rich enough currently to extract it, but it could be done. There is no need for a central bank for gold, and this lack of a need for an authority is what makes the gold sound.
The role of the difficulty adjustment is to decide a timeframe for the initial distribution of coins (with the halving plan), and to have a predetermined block time, which is needed for payments. It is not fundamental for the soundness. The soundness is that nobody gets coins for free, and the resulting lack of need of an authority. So what would happen if there was no difficulty adjustment? This is a thought experiment, but it can be useful for the understanding. With increased coin price, the miners would put more effort into mining, and the time between blocks would decrease (block rate increases). It would go down to one minute, a few seconds, and we would get lots of orphans and reorgs. We would end up with miners producing hundreds of blocks per second, and finding a block is for a miner just half the work, because most of the blocks he finds will be abandoned, the effort wasted, adding to his cost. But the coin would still be sound. The halvings would come weekly, and all coins will be mined in the short time, but the cost of newfound coins would be the same as now, approximately the market price. We need the difficulty for various reasons, to stretch out the coin creation, and give the market time to adapt, and to make sure we have a reasonable block frequency for the payment function. Summa summarum, the difficulty adjustment is needed, but it is not essential to the soundness.
I could construct examples from production of consumer goods that show the same, first value from consumer preferences, then the cost follows (and volume, if practical).
The enforcement of the developer fund (in Bitcoin Cash) increases the mining cost, and the other cost factors have to be reduced, mostly power but also the number of asicminers, thus the hashrate will go down.
Enforced here means that it is included in the rules for valid blocks. On a higher level, it is not enforced, because there could be a split and the market could choose the alternative coin, so the market still decides. The change which diverts some or the subsidy for mining to a fund and establishes an authority, will not stop the world from having sound money, if the world wants it.