Your question is awfully loaded. So first, a few clarifications-
The proper question is not whether or not meta-analyses are flawed. But rather, are meta-analyses more flawed than your average scientific publication? Bear in mind that all forms of scientific publishing are inherently susceptible to falsification. When you're talking about a "flawed" publication you need to define what you mean more precisely. Ostensibly a paper that has gone through peer review and has been accepted should be free of gross defects in methodology. Otherwise, the problem is not really on the paper, but rather on the community that allows poor-quality papers to be published.
Are meta-analyses falsified more often? Are they retracted more often? You haven't said exactly what you mean by low-quality, and so we can only guess at what you mean.
However, I can answer a variant of your question:
Why are statistical meta-analyses useful?
Statistical meta-analysis is useful because single studies are never authoritative. Making authoritative statements requires replication. To see why, let's look at the commonly used p-value. These are used as a way to differentiate the effects of random sampling from true experimental effects between a control and experimental population. In any experiment, there is a chance that an observed effect is purely due to sampling error- suppose you're testing whether or not a chemical causes cancer in mice.
Ideally you'd use enough mice so that minor variations between your experimental and control group don't impact your analysis, but this is not always the case. Even if you use a hundred or a thousand mice, there's some small chance that you were just unlucky and happened to pick a hundred or a thousand mice that were genetically predisposed towards developing cancer. The ex post facto likelihood of this being the case greatly depends on the final difference between the two groups, and this is essentially what is measured by p-values. A smaller p-value is better, and implies there is a smaller chance that the observed experimental difference was due to sampling error.
Now, particulars aside, just know that certain fields of study use the p-value as a minimum barrier to entry for scientific publication. For example, someone might say that for an experiment to be meaningful it must achieve a p-value of less than 0.05. Suppose you run a study that achieves a p-value of 0.045. It's suitable for publication- but having a low p-value doesn't mean that you've got a bulletproof result. All it means is that the probability of your result being skewed by sampling error is "low", but "low" might 50% or higher.
A recent study in psychological science was published that estimates the reproducibility of experimental effects based on p-value. The Minitab Blog interprets this study for us statistical laymen. The basic result is that people sorely overestimate the reliability of experimental results with low p-value. Even good studies with very good p-values (less than 0.001) were not reproducible over 1/3rd of the time. The bare-minimum studies that had a p-value near 0.05 were not reproducible about 2/3rds of the time. The following chart is from the Minitab Blog:
At this point, the answer to my modified question should be clear. Modern science is a statistical endeavor, and (given the statistical tools available to us) individual studies are rarely if ever high-confidence results. Thus, statistical meta-analysis are necessary for making high-confidence claims. This leads to a high citation rate because it isn't the first or second paper on a subject that is authoritative, it is the culmination of several studies that allow researchers to be authoritative.