You do not use surveys to learn about gravity. That would be stupid. You use surveys whenever there is no better way to get the data you want. We have better ways to learn about gravity than surveys, so we use those. This is true for all scientific methods we have: All are not perfect (some are better than others, though) and all are not appropriate to answer every question.

(I know very little about psychology so I’m going to put on my social scientist hat.) The Large Hadron Collider can tell us nothing about which political issue people think is the most important one (one of the variables needed for Agenda Setting research, for example), so even though it’s a great tool to learn about gravity, it’s not a great tool to learn about Agenda Setting.

fMRIs are currently also about as useful as the LHC when it comes to answering questions like that. fMRIs are not very precise, we don’t understand the underlying system (brain!) thoroughly enough, they are expensive so we can’t look at very many people and have a representative sample.

They are just not good tools when it comes to answering certain questions and surveys become then our only realistic option, warts and all. (Some warts every good social scientist knows about: social desirability bias, reactivity, ceiling and floor effects, …)

So, Agenda Setting. The hypothesis is that issues about which the media reports a lot are also seen as important by the recipients. If you want to answer that question you have to do a quantitative content analysis and a survey. There is no other way to get to that data.

Surveys are not dubious tools. In the context of this research question, for example, an fMRI would be a much more dubious research tool.