It is a restriction from operating a particular piece of machinery on (essentially) public land, isnt it? You can still travel by the same mechanism as long as you are not the one operating it.

That seems fairly different from restricting travel by air.

Freedom does not mean you are allowed to do or refrain everything you want because you have to respect the freedom of everybody else. Therefore your freedom ends when it limits the freedom of somebody else. It is not hard to argue that you are (probably) limiting the freedom of other people to walk safely across streets when you are driving without license or after having a few drinks. Freedom and prohibitions are not mutual exclusive.

No, we're not. We're just saying that if they get caught driving without a license, they'll likely be prosecuted for that offense. They're perfectly free to try not getting caught. People on the no-fly list will be physically restrained from boarding a plane.

Actually you can drive a vehicle all you want without a license as long as you don't do it on a public road. The license doesn't allow you to drive a vehicle; it allows you to use public roads that have certain rules, for safety mostly, associated with them. Your license proves that you understand said rules and will obey them while on the public road. A lack of a license shows you cannot be bothered to follow the rules and are a danger to everyone else on the road. Therefore, you must be removed from the road for the safety of the others. Preventing an unlicensed driver from using a public road is more about the other people on the road than the single driver. Your freedom doesn't allow you to be a danger to others.

For instance, in many US states you are not required to have a license to operate farm equipment on a public road. There's likely many reasons for this but the rules of the road in those areas do not restrict you in those cases.

If I had a large enough tract of land that a shortcut going through the middle was beneficial to people around the property I can put up a sign at the entrance that states if you wish to use my road on my land then you follow my rules. It's the same principle.

Also, many a young teenager legally learned to drive a vehicle, cars or motorcycles, on private land even though it would be illegal for them to do so on a public road.

1. The exam is qualifying you to operate heavy machinery in public.

2. You can re-take the exam if you fail it the first time.

3. You can operate a bicycle or be a passenger on any bus or train without a driver's license.

Your argument is not applicable. Riding a plane does not involve operating a giant machine on a public road around other giant machines and pedestrians.