Not sure I would agree with "nobody would choose to be self employed" in the general case.
A lot of people like the freedom, importantly the reduced NI contributions (what's the basic state pension worth, anyway, against building up your own investments?), the ability to concurrently freelance for other companies, etc.
SE also enables a lot of things to be offset against your income tax, like travel costs from your home to the site you happen to be currently working at - something that is absolutely prohibited in the PAYE case and which can be worth a great deal of money.
This is a controversial statement but (as someone who has employed many people over 30 years of being in business) I think that good smart resourceful people generally prefer SE and the less good and less resourceful prefer the security of PAYE and the ability to sue if they get the push.
I don't really know anything about GA flying instructors but I've met a fair few; many were on a £10/day retainer and some were on a zero retainer. I am sure they would have all preferred a PAYE position on £35k with BUPA chucked in but few flying schools can afford that, knowing that the FI is going to leave the moment he gets an airline job. There lies another paradox: if a PAYE person gets the boot he can sue for all sorts of things (after the first year, and at any time if he can allege certain things) but if one day he simply walks out the employer cannot do anything and still has to pay the person for time actually worked right up to the last day.