Having finished an introductory course in GR, I started reading a bit about the modified general relativity theories, especially f(R) GR and scalar-tensor theories.
However, I am unable to understand the appeal of these theories. Are they studied purely for the sake of studying them, or are there underlying reasons?
For example, in Brans-Dicke theory, it would seem that it is compatible with the PPN parameters only for some "unnatural" values of its parameters ($\omega$, in my textbook). Furthermore, it seems to me that it not extends general relativity, in the sense that it struggles to explain what GR does gracefully, and does not provide anything new for the "problematic" parts of GR (namely inflation, dark matter or cosmological constant).
Am I missing something? If the question is too broad, I'm okay with an answer concerning only Brans-Dicke theory. I just want to know if there is a specific goal these theories are pursuing, or they are just developed to "explore" possible alternatives to GR without any real goal in mind.
Edit : Initially, when I was still learning GR and only had heard about modified theories, I thought that their aim was to give a theory that would not require dark matter or a cosmological constant to account for observations, or that would not require an inflaton field for inflation to occur and so on. Now having read a bit around the subject, I have the impression that few explore these possibilities, hence my question. Please take note that I have only recently started reading on the subject, so I may have gotten a completely wrong idea.