"But, if you do see 10% significance(/90% confidence) in a small sample, this is just as good as 10% significance in a large sample". That is not true, strictly speaking. You are assuming that small sample describes the underlying distribution well. But this may not be the case due to non-normality of the distribution itself or potential biases
The sample has to represent the population, that's fundamental. If the sample is so small that it can't characterise the population distribution, then you have a problem anyway. If you're measuring a events that happen 1% of the time (or 99% of the time), a sample of 100 is not nearly enough.
If you chose an appropriate non-parametric test to cover an unknown distribution with a small sample, it maybe would have zero power (impossible to give a significant result)
