My favorite recent application: two-parameter persistent homology for drug discovery (link to pdf of talk: https://www.ima.umn.edu/materials/2017-2018/SW8.13-15.18/274...). Frankly I find two-parameter persistence very hard to interpret, though I hope to spend some time on it this summer. But it's undeniable that the work described in the link is an application that can't be reduced to clustering.

I also feel that describing Mapper as 'just a clustering tool' is not really accurate; I'm getting good results from using Mapper for feature discovery in some specific domains where clustering has truly failed because traits lie on continua in a way that renders usual clustering muddy and useless.

Edited to add: here's another interesting paper, about subgroups of type 2 diabetes patients: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780757/ They use Mapper to find 'clusters' and then go back to more traditional statistics to test significance. I don't have the data so I don't know if clustering alone would have worked.