But when people are looking at N=x, most don't realize that N<30 is usually in a completely different category than N>=30. You almost shouldn't look at it as "N".
Novice "statisticians" are just (very) limited in the tools/formulas/methods available to use, because so many (entry level/basic/standard) statistical methods are only valid for normal distributions (or other constraints on data, that people typically don't check for).
Without details stated up-front, most people will (wrongly) assume that a normal distribution automatically applies, even if they don't know what that means. Similar to situations where people ask for the average/mean when they should be asking for the median.
The data isn't useless, but needs strong context and disclaimers.
I’m also fairly certain you don’t understand what a “random distribution” is yourself. That’s because there’s no such thing. There’s a normal distribution, binomial distribution, Poisson distribution etc, and they all involve randomness. But there’s no “random distribution”.
So maybe you shouldn’t be quite so quick to judge “novice statisticians”, and what those imaginary people you mention a total of five times may or may not “wrongly assume”, or “don’t know”, or “are limited in”, or “don’t check for”.
And I didn't mean to imply that I'm any better than a novice. I just know enough to know to always check that assumptions for any given test needs to be valid. (It's been a few years since I've had to use any of this in a professional capacity.)
But is 30 plenty? Or is it sufficient?
As I remember, normal distribution usually requires a sample size of N=>30. (As in 30 is the minimum.)
If you think it depends on something, go ahead and say so and I'll constrain the thought experiment.
IAmEveryone (user w/ sibling post) is correct in that I'm referring to the fact that effect size affects statistical power.