Why are meta-analyses the most quoted type of research paper despite being often flawed? Meta-analysis represents the statistical pooling of several individual studies focusing on a specific research question, ideally conducted within the context of a systematic review of the scholarly literature. 

Several examples of meta-analysis are available, with the first ones already appearing in the mid '50s, despite this term being proposed first by Gene Glass.

Indeed, it appears that meta-analyses continue to have substantial success in the scholarly literature, and often appear among the most quoted types of research design. Yet, a plethora of meta-analyses of suboptimal quality is being currently published, and this unfortunate trend does not appear to cease.

Which are the main reasons for this success? And, most appropriately, is this scientifically sound and reasonable, given the epidemic of meta-analyses often of suboptimal quality (Ioannidis 2016) or overlapping in content (Biondi-Zoccai et al, BMJ 2006)?

Disclosure: I am the first author of Biondi-Zoccai et al, BMJ 2006, and I have coauthored dozens of meta-analyses.
You have it backwards.  Meta-analyses are not heavily cited despite frequently being flawed; rather, they are frequently flawed because meta-analyses are heavily cited.  

Because meta-analyses often were high-impact papers, many people with poor training and little experience tried to publish their own meta-analyses, in the hope of boosting their C.Vs.  It's (mainly) this flood of incompetent authors who are publishing flawed studies, and dragging the whole field down.  


  The increase is a consequence of the higher prestige that systematic reviews and meta-analyses have acquired over the years, since they are (justifiably) considered to represent the highest level of evidence. Many scientists now want to do them, leading journals want to publish them, and sponsors and other conflicted stakeholders want to exploit them to promote their products, beliefs, and agendas. Systematic reviews and meta-analyses that are carefully done and that are done by players who do not have conflicts and pre-determined agendas are not a problem, quite the opposite. The problem is that most of them are not carefully done and/or are done with pre-determined agendas on what to find and report.    


--We have an epidemic of deeply flawed meta-analyses, says John Ioannidis

Eventually, hopefully, journals and authors will become more aware of this and the poor-quality reviews will be ignored, correcting the problem. As evidence for this, we see a number of guidelines and resources for improving meta-analyses becoming more widely used over the past few years:


IOM
PRISMA
MOOSE