walk into any university, go from one faculty office to another, ask each professor what a p-value is and the overwhelming majority won't give you even a half-decent definition (I did this and can attest to it)
you know why? because p-values are far more complex than people care to admit. Most statisticians cannot properly use it! There are ongoing "ideological wars" over what it actually means. Even the founders Fisher etc argued all the time about them. If you used p-value correctly, you would almost never be able to find anything, not even valid results.
So people have to "bend" the truth a little bit. Nowadays more often than before, the truth gets bent out of shape.
But yes, society doesn't function well when people are corrupted.
Your distribution is not normal - it almost never is, now you have to argue that the method is still robust - there is no proof that is indeed robust as you claim. Then your measurement is a bit biased, see on Tuesdays the measurements do turn out a little bit differently, but most often does not matter, so you skimp over that as well.
Statistics is the wrong approach because if you did everything correctly and stuck to the letter of it you only end up hurting yourself. You'll make fewer of the valid discoveries that you make when you bend it a bit.
This is the fundamentally wrong thing about it! Strictly sticking to the rules will make you weaker. Bending statistics a little leads to more valid results.
If it is not normality then something else. Every statistical measure makes assumptions, most of which never quite hold true. That was my point. When someone uses statistics they always fudge things a bit. Many times does not matter, if you were stickler for "precision" it would not work.
IMHO it actually suggests we need to improve the average person's educational level