Yes, the Kurds are pumping up the oil and using it to fund their military machine. Hence the strained relationship with Turkey... They really dislike Kurds.
The US denies oil revenue to a crazy dictator selling it to fund his crazy antics and prevents Russian proxies from capturing the fields to fund their crazy antics all with minimal troops.
It's not as if the alternative would be that the oil revenue is used to buy happyness, health and prosperity for the Syrian people.
In a time where the questions they used for age verification could not be quickly looked up on the internet.