Regarding your inquiry; because it allows for the original author to do mutations and calculations on (your) data carried or distributed by untrusted third parties. This way someone could for example provide updates while being at less risk. Various asymmetries between the amount of data dumped and the amount of resulted output could also be helpful in certain niche scenarios.
To me, while I agree such a use case might make sense in a very narrow context, homomorphic encryption currently supports a limited subset of resources normally available on a computer and even doing basic operations on a small amount of data takes a very long time, adds a lot of complexity, custom information formatting, etc.
As such, in my opinion, unless I am something, homomorphic encryption would be a poor fit for a use case similar to SecureDrop’s use case.