Is it time to be less rigid about mixed-method analyses?

As I have mentioned in my About me page, my background is in economics, which is thoroughly embedded in quantitative analysis. There isn't much qualitative analysis as understood by non-economics disciplines. One could make an educated guess that, quantitative data analysis will fail to incorporate a lot of pertinent qualitative considerations; conversely, qualitative analysis has severe limitations in the types of insights it can provide. Unfortunately, good quantitative analysis is time consuming. Especially when an analyst has to consider all the potential issues and concerns, it can take a few rounds of implementation to obtain the most accurate estimates.

While I am marginally less experienced in qualitative analysis, I do not find it to be as time consuming or perhaps even as complex in comparison. It is not necessarily a bad thing, depending on the situation - after all, speed and rapid delivery (keeping quality fixed) is universally considered preferable.

Listening and reading the news about current debates, it hit me like a brick wall why there is so much demand for qualitative analysis. Currently, there are discussions about the harms of social media on mental health and life outcomes. The defense for social media is obviously going to make the claim that harmful effects do not exist; I have not read anything about the e.g. quantitative analysis conducted to reach such a conclusion, but it wouldn't surprise me that any quick calculation results in null effects. This is where qualitative analysis can be useful, because if e.g. court cases are on-going, decision makers require results now, which means qualitative analysis might be their only option (thus testimonies). Unfortunately, because they are taken as anecdotal evidence, they are considered less convincing compared to rigorous quantitative analysis using large datasets.