The plane is invisible which would be good for stealth but you can see Wonder Woman flying it. My question is, what is the point of having an invisible aircraft if you can see the pilot?
I would prefer an in-universe answer.
There are a wide variety of reasons an invisible plane would be useful. But firstly we need to state what may seem obvious;
In addition to the obvious benefit of having an invisible mode of transport, there are other reasons why her plane is useful;
The plane is described as being able to generate "invisible missiles" that simply explode without warning.
Her plane is described as being able to travel at speeds in excess of 2000mph, vastly faster than she can fly unaided.
Wonder Woman answers this question herself here in Wonder Woman #197
Interviewer : If you can fly why do you have an invisible plane?
Wonder Woman : That's a very fair question. I have an invisible plane to carry my invisible luggage
No honestly, I keep the plane in case I have to carry passengers or cargo
She was a character who was over the top, a woman made from clay imbued with powers from the gods, living on a island of all women, who would come to the Man's World with a message of peace but completely capable of kicking any man's butt.
She had to have a ride that was over the top as well, one-upping anything made in the Man's World. Her plane could do everything ours could AND was invisible.
Just bear with me a moment:
You have to remember that comics are a visual genre and as a result, you are supposed to accept with the same grace we did when action balloons like POW!, CRASH and the famous SHRAKRADOOM! (from Thor and Walt Simonson's run) would appear on the pages that Wonder Woman and her passengers, while being drawn for your enjoyment, are actually invisible while inside of the Invisible Jet.
WE, THE READERS, SEE WONDER WOMAN AND HER PASSENGERS. In the comics, they don't. Otherwise kids would have been spending their hard earned pennies to watch Wonder Woman board her invisible jet and then just watch scenery until she arrived at her destination. In the Wonder Woman movie referenced below the entire flight scene is less than 30 seconds of screen time. No one wants to see an invisible jet...well they do, but only for a moment.
This would be the same for the television series. Invisibility is great as an idea but when you have to show it on screen or on the page, it becomes problematic. No one wants to see a blank page for very long. It is possible her ship was the very first comic depiction of a cloaking device and like in Star Trek IV, when they leave the cloaked ship, they become visible suddenly.
This is the suspension of belief for the sake of the story. Her jet is invisible from the outside and so is she while she's in it. Just run with it.
Wonder Woman, 2009 (Animated Movie Release)
From 2009 animated feature, Wonder Woman. The Invisible Jet from above as seen while leaving Paradise Island. Note the lack of visible passengers, yet the plane is still translucent to the background.
Inside of the Invisible Jet is NOT invisible, which makes perfect sense if you wanted to have a plane with a control interface. If your plane is mentally piloted (as the Pre-Crisis device was supposed to have been) then you don't need to see anything inside.
From 2009 animated feature Wonder Woman. The invisible jet arriving in New York with Steve Trevor and Diana onboard. Note the invisible nature of the invisible jet with its invisible passengers.
My own take on this....I have to laugh. I believe that an originator of the idea when asked how WW gets around said "...she travels on the invisible plane" i.e. like on the "spirit plane". But some idiot illustrator took his words literally and he drew an invisible aircraft. Which just seems daft. To travel through the "invisible plane" and so appear anywhere feels just so much more appropriate - Goddess-like - and properly cool. ...whilst siting in mid-air in an invisible aircraft... really!!!