Air Traffic Controller here. You are correct. There are many airports that are just a runway and have CTAF (Common Traffic Advisory Frequency) where pilots ad

Air Traffic Controller here. You are correct. There are many airports that are just a runway and have CTAF (Common Traffic Advisory Frequency) where pilots advise each other of their position, heading, intentions, etc. ATC can give clearances to aircraft landing and taking off from such airports, but the clearances only apply in controlled airspace, usually starting 700ft above the ground. ATC can also make sure there are no other IFR traffic for aircraft requesting clearances, but if it's VMC (visual meteorological conditions), there could be VFR traffic for the IFR aircraft that ATC is not talking to.