I don't think there is a large intersection between these two groups at least in Europe. Price sensitive people didn't buy SUV. Better-off folks who buy SUV unlikely to be significantly affected by this price increase. In the US it may be different because most cars on the market are SUV/tracks and it's harder to find a small car.
I'd say that a 2022 Subaru Outback is not a "big SUV" - the EPA classified it as a small SUV (medium starting 2026), and it had a crossover station wagon body style.
Now I do wonder about those people who buy a Chevy Tahoe, Ford Expedition, or Toyota Sequoia and then complain about gas consumption...