We do have smaller regional airports in the US, but those smaller airports do still have TSA-staffed security if they serve commercial flights. The TSA considered eliminating security at those smaller domestic-only airports back in 2018, but after it hit the media, they reversed course on it.

The only exception would be airports solely for things other than commercial flights, like hobbyist pilots/flight schools where people are flying their own planes, or airports serving only government/medical/whatever "essential" traffic. Airports that don't have TSA-staffed security are still under TSA jurisdiction, and have to pass regular inspections by TSA to ensure their own security's at a sufficient level.