This "expert" has never flown a plane in his life, I expect.
-Smoothing out traffic flow patterns doesn't work because planes still have to get lined up in the proper direction with the wind
-You can't land three planes at once because they wouldn't all be facing into the wind properly
-Go-around procedures conflict with arriving traffic from other radials. If a plane has to abort a landing, it's flying back up towards the arrival pattern of another plane on the circle.
-Very large aircraft would have to immediately begin turning on touchdown, at high speeds, while they have minimal traction. This would result in significant instability which is very hazardous at that speed
-Rate of turn would only match the runway radius at one exact speed/bank angle combination, aircraft would therefore often be drifting laterally in relationship to the runway
-Contaminated runways would become suicidal
-You can't spread the noise issue out because planes need to land into the wind
-Multiple parallel runways already solves the simultaneous landing issue in a safer fashion
-Emergencies during the takeoff run, particularly engine failure, become much more hazardous due to the turn. Aircraft aborting a takeoff have to follow a curved path in what is already the most time-critical and life-critical operation in a pilot's career. (say the term "v1 cut" to any jet pilot and see the look on their face)
-The actual heading on liftoff now becomes difficult to accurately predict, as takeoff lengths vary based on numerous factors. This ruins traffic flow. "North-ish" isn't good enough for departure procedures at congested airports
-One gigantic circular runway actually requires more pavement, not less. This is like 5th grade geometry stuff.
edit: - Heck, crosswind operations actually get harder, not easier. Following a curved path, your angle to the wind will be shifting through the flare process. Sure, you're angling in to be mostly pointed into the wind, but the fact that the relative wind angle is changing is what adds the challenge.
This concept is less safe and less efficient and more expensive. On a day of very calm winds, some of the problems can theoretically go away but this still becomes a nightmarish problem for air traffic control to solve. Part of the reason arrival paths follow neat lines is because it's incredibly hard to manage hundreds of aircraft arriving from random directions.
edit2:
-Terminal structures can only reasonably be built inside of the ring, necessitating tunneling under runways for entry roads.
-Runway maintenance becomes more complicated with the banked surface and difficulty in defining closed areas vs active ones
-Emergency landing operations involving brake failure or other control issues render the airport entirely unusable - emergency stopways found at the end of straight runways are not usable on a circular runway