BTW, I didn't address this...
lets say there is a football skill
Vince Lombardy would have a very high skill in this, but relatively low stats; he would be killed if he went out on the field.
His players would be less knowledgable of the game of football than their coach, yet would be able to play the game much better
I would disagree with this. Vince Lombardy has a different skill other than "Football". In real life, there are many great football players who make lousy coaches. Vince does have some skill in "Football", but what he also has is a skill called "Coaching", and this is very high.
In Traveller terms, this would probably translate to the "Instruction" (first seen in Book 4, I believe).
There are many examples of stats overpowering skills in the real world..
Thats were coaches/mentors/teachers come from.........if they have training skill, so much the better.
Again, I would disagree. There are instances where stats overpower skills, but it's typically very high level stats overpowering low level skills.
Raw, natural talent won't automatically "train" you with specific skills. Thus, the old saying, "There's no substitute for experience."
If you score high on an IQ test (high INT), does that automatically mean you know how to program an intricate piece of software needed for a large company?
Nope. You need Computer skill for that.
Your raw natural talent may allow you to figure out how to put together your own desktop PC (an example of high INT stat overpowering low Computer skill), but your high INT isn't going to help you with all the ins-and-outs, pros-and-cons or creating a viable piece of software for a large, multi-national corporation.
That job requires experience. It requires skill. Not just high INT.
Another example...
Let's say you just graduated from Harvard Law. You've got a very high EDU score now (and some skill in Law).
Does this mean you can pilot the space shuttle? Does this mean you can repair the reactor on a US Naval submarine? Does this mean you can perform brain surgery?
See where I'm getting at here?
If you allow a huge DM from having a high EDU, then you're saying that a high EDU allows you to do
ALL OF THOSE THINGS at a very high level.
Stats are broad-based natural ability.
Skills are focussed experience in a specific area.
Just because you have EDU-12, you should not be able to pilot the space shuttle as a Pilot-4 would.
Just because you have EDU-13, you should not be able to repair a submarine reactor as an Engineer-4 would.
Just because yo have EDU-14, you should not be able to operate on a human brain as a Medical-4 doctor would.
You need
skill, training, knowledge, expertise in these areas to succeed.
This is why a GM should always be wary of a task system that overpowers Traveller skills in favor of Traveller stats.