I'd like to make a pretty straightforward scope/tractability/neglect argument in favor of more anthropics research. I think that assessing the validity of the doomsday argument (that most humans are among the last 99.9% to ever live, so we should be starting from a 99.9% prior that there won't be 100 trillion humans) in particular is high impact. I would love to hear others' thoughts, including disagreements.
Scope: My understanding is that there is no consensus on whether the doomsday argument is valid. Cause prioritization is a central question for the EA movement, and I'd argue that the validity of the doomsday argument is a really important consideration. In particular, if we come to a consensus that the argument is invalid, then the case for longtermism seems really strong to me. (Holden Karnofsky has started laying out the argument in a series on his blog; link to first post.) If however we come to a conclusion that the doomsday argument is valid, that bolsters the case for prioritizing more short-term causes, such as third world poverty and animal suffering.
Tractability: Anthropics is incredibly confusing. But also I do get the sense that we've started thinking more clearly about it over the last 20 years. I expect this progress to continue. It seems to me that there's lowish-hanging fruit in particular in laying out the various assumptions (SSA, SIA, and variations of these) with mathematical rigor. In theory, this ought to help reduce disagreements ("Is the doomsday argument correct, under SSA?") to variations in the particular assumptions being made, which will allow us to think more carefully about these questions.
Neglect: It seems to me that not many people are actively thinking about anthropics. I could be wrong, but e.g. most of the well-written anthropics posts on LessWrong seem to be by one person (Stuart Amstrong). My general sense is that we as a community are kind of scared of touching anthropics, because it's really confusing. I think several more people thinking seriously about anthropics would increase the number of people thinking seriously about anthropics by a factor of 2 of so.