For one particular example where homoiconicity makes reasoning about programs easier, consider an important reasoning method called abstract interpretation:

https://en.wikipedia.org/wiki/Abstract_interpretation

Using abstract interpretation, you can derive interesting program properties. The uniformity and simplicity of Prolog code, as well as its built-in language constructs like unification and backtracking, make it especially easy to write abstract interpreters for Prolog.

Here is a paper that applies this idea to derive several interesting facts about programs and their meaning:

Michael Codish and Harald Søndergaard, Meta-circular Abstract Interpretation in Prolog (2002) https://link.springer.com/chapter/10.1007%2F3-540-36377-7_6

Abstract interpretation is also applicable to other programming languages. However, it is much easier to apply to homoiconic languages like Prolog.