Increases in supply also increase consumption, we use lots of cheap stuff, but not very much of expensive stuff.

This would be true but you're not accounting for OPEC and other groups (e.g. historically the Texas Railroad Commission in the United States, not sure how relevant they still are) to balance production and price per barrel to what they think is agreeable.

Oil hasn't been supply constrained since the 50's, it's price is largely based on what producing countries agree on, as well as geopolitics.

Additionally, governments levy a decent amount of taxes on certain end products such as gasoline. They might very well, as they have in the past, decide to simply up their tax revenue as prices of crude and derivatives go down.