To prove or disprove your hypothesis, we can look at historical gas prices.
In today's dollars (adjusted for inflation) the US average gas price stayed below $2.75/gal from roughly 1986-2002. Then they broke through that barrier, only ever going below it again for two brief moments in 2016 and in 2020. Most of the time since, they've been well above $3.50, and above $4 sometimes. [1]
If you're right that demand for gasoline is highly elastic, meaning people adjust their demand in response to price, then since gas prices got much more expensive, we should expect that gas usage decreased. Have we seen this? (No. [2]) Of course we haven't, because somewhere between 63-67% of people in the US and Canada live in car-dependent suburbs.[3] These cities and towns, in addition to most rural areas, are fundamentally car-dependent and cannot function without daily car use by a majority of residents. The only way for our society to consume less gasoline would be mass electrification of private transport.
And notably, even the recent increased popularity of EVs in the post-Model-3 era isn't manifesting in the data [2] in the form of decreased consumption to my eyes. Perhaps for every new BEV out there not using gas, five people traded the cars they used to drive for inefficient, huge SUVs.
1. https://www.inflationtool.com/adjusted-prices/us-gasoline
2. https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=w...
3. https://lcau.mit.edu/research/american-suburbs-project
