>A shortage necessarily means that if you make more of something, you're guaranteed to sell it basically instantly, so there's already an incentive to increase production.

This is patently false. Every oil reserve around the world has a cost per barrel of extraction. At $60/barrel many of them are shut down.

If you fix the price at $60 and demand goes up, you’ll end up with shortages and producers won’t be able to fill the gap.

It is very rare to have a market of physical goods where the cost of production is fixed and supply is effectively limited. For every other market, the price needs to go up to entice investing in making more supply.