you guys seem to love the legal stuff
No I don't , just happens to be part of the job.
other than the immigration officer who wants to know the purpose of your stay - it seems like nobody afterwards cares about it. Neither the TSA, nor the flight school, nor the examiner
And it isn't the examiner's job to care about it, however some FSDO's (regional FAA offices) have required their Pilot examiners to ask for visa's.
Not all, some. I'm not sure I agree about that practice, they are examiners and not trained to be the visa-police.
The Immigration officer cares and so should you. He has the final authority as to allowing you to enter the country.
A visa DOES NOT (repeat, DOES NOT) give you the RIGHT to enter the US, it gives you the privilige.
In hindsight it seems like a lot of money...."
No it is not. You need a visa for certain holiday destinations don't you?
There is a reason (probably financial) why you did your flight training in the US.