You make it sound like those studies were bad because the sample size was too small. In reality bad study design or having an unrepresentative sample are more common issues.
I think they go hand-in-hand. People naively apply intro-level statistics to messy real-world problems and then think they need an orders of magnitude smaller sample than they would need to even hint at the possibility of an interesting effect.
Neither a bad experiment nor an unrepresentative sample will be helped by a larger sample size, though.
True, though no sample is ever truly representative along every dimension. Even when a lot of effort is put into making a sample as representative as possible, there will be variance in all the potential ways the sample can diverge from the population; this variance seems to be consistently underestimated.