The pilots do fly the plane, but much of the flight can be automated, like the terminal phase where the aircraft MUST meet certain gates in order to be allowed to continue on an approach.
There are probably YouTube videos of commercial flights filmed on the flight deck. You can see exactly how confusing and busy it gets at various stages of flight. We live by checklists and approach and departure procedures.
Aviators must learn how to communicate in a very precise language and listen to specific calls from ATC. Violating a directive from ATC can cost a pilot their wings. Pilots are responsible for the safety of their aircraft but ATC is responsible for the safety of all aircraft on their scope. It is a VERY congested airspace and pilots must be aware of all that is going on around them.
I am a pilot too. I have flown an SEL with no help what so ever and have on many occasions flown in controlled airspace and have no problem doing that. Hell, I can do it all day long. It’s actually fun. I guess I am weird.