With rising oil prices, if countries decided to curtail their consumption - akin to a directed economy - to reduce purchases to a minimum and even refusing to buy above a certain value, what could that cause?
The first reaction I’d expect would be production cuts to hold the prices but, technically, those are already happening. Demand is just not following.
As for impacts to the local populace, you don’t need to imagine a theoretical outcome. You can see live versions of it to different degrees happening in several place in the world:
The least extreme is the USA where small businesses that depend heavily on fuel are simply stopping work because they would lose money operating with the current prices of fuel. Elsewhere costs of everything delivered by truck or rail (both run on diesel) continue to rise as the transportation costs increase. If this price keeps up, its going to get particularly bad this winter as much of the northern states still rely heavily on heating oil for heating, which base petroleum is chemically identical to diesel and thus facing the same fuel cost increases. Apparently with the current cost of heating oil an average winter heating bill would be $30/day.
A moderately worse version is Russia which is experiencing fuel shortages because of its invasion of Ukraine. There are long queues for fuel in many parts of the country, and ration limits have also be introduced in some places.
The most extreme version would be Cuba where the USA (is being stupid) and blockading the import of oil to the nation causing widespread power outages, etc.
As for the causes on world oil prices, unless the countries would represent a notably large share of the petroleum consuming countries, it would have almost no impact on oil prices globally. All countries capable of producing, refining, and delivering oil right now are running at max capacity.