Airplanes have "flown themselves" for a long time because autopilots are generally glorified cruise controls. There's no intelligence or automatic decision making. They fly courses, altitudes, and speeds programmed by the pilot(s). It's a very manual process. You don't just hit "fly me there" like with FSD and you don't just dial in a destination like in a car GPS.
Airliners do have tech to avoid collisions. TCAS has been around since the early 90s. If two planes with TCAS detect they are on a collision course, there are automatic responses the planes will make to steer away from one another.
The vast majority of airports in the US do not have "people on the ground watching everything". At these smaller airports the pilots handle it themselves using eyes and radio, just like drivers at a roundabout. And many people flying those little airplanes VFR never file flight plans no matter where they're going.
Private plane pilots are encouraged to file flight plans and many do when flying any distance. The traffic around most private plane airports is very low. Any airport where traffic is getting anywhere close to 1/10 what you would encounter on a city street, there is ground control monitoring air traffic. Every city also has a regional air traffic center that tracks all air traffic in the region, even flying in and out of smaller airports. They aren't necessarily in contact with those aircraft, but the aircraft are being tracked. If one of those aircraft starts getting close to commercial air traffic they will be contacted.
I worked in the avionics end of the aviation industry for a while. I've watched that same air traffic data the ground control people monitor in the lab. I could sit there and watch every plane in the air over the Puget Sound area on one screen.
Planes can go dark on that system by switching off the transponders. That's what the 9/11 hijackers did. There was talk after the attack to put in radar in the ground systems to detect aircraft with their transponders off. I don't know if they did that or not. I've been out of the aviation business since 2001.