I will go out on a limb here and suggest that you are correct. Too many studies are too small to have meaningful results. I fact a google search for [scientific studies not reproducible] turns up some scary results. One is that only 10-30% of studies published in journals can be replicated.
There are many reasons for this, but poor research design is a main culprit, including too-small sets of subjects.
As to the reason for the small sample sizes you can point to both money and time. It takes more money and time to sample a larger set in all but trivial situations. But it can be hard or impossible to get a larger body of subjects for many studies. The potential universe of subjects may be widely distributed in space but sparse within the larger population. Sometimes many factors may be required for acceptance, leading to rejection of many. Some studies may just run up against opposition from the population due to many factors, including simply that it takes effort on the part of a subject.
In addition to the size factor is that many studies rely on using students at the same university as subjects. These folks are not representative of the population as a whole unless the population itself is defined to be university students.
Another problem with samples is that the subjects are always assumed to be "randomly" chosen from the overall population, but it is very difficult to assure that in many cases. This is the problem with using university students, in fact.
Small sample sets are perfectly natural for preliminary studies that can give direction and provide refinement to the design of a larger study. But, as you suggest, it is hard to extrapolate results from a small sample to a large population if that population has much variability.
Moreover, small studies cannot, by the nature of statistics, capture subtle effects. If you are trying to determine if more "mumbles" have characteristic "A" or characteristic "B", then a small sample size of "mumbles" will work if, indeed, the actual population breakdown is 70-30, but statistically unlikely if it is 57-43.
For reasons like the above, many researchers are moving from a standard 95% confidence interval in studies to, perhaps, 99% (or more). This helps weed out many of the design issues that cause the problem of non-reproducible studies. But that is risky for students who want and need some results to put into a dissertation and are limited in both time and money. But while small sample size is fine for initial, exploratory, studies, it is not for determining the state of reality.