However the closer you get to an n=30 the more signal strength is required to achieve p<.05.
That is a result of the uncertainty of the sample being representative of the whole population as n becomes smaller.
If the n is less than 30 then different statistical tests are used because of higher possibility of having a non-representative sample due to the variability in sampling.
As you point out the population in question is a distribution of values. The smaller the sample size the more difficult it is to get a sample that is representative of the true distribution. It is that increase in uncertainty that requires a stronger signal to compensate for the increased uncertainty.