It is largely a matter of training and temperament if you think it's more rewarding to start from the observations of current phenomena that all have some uncertainty and laboriously work backwards to predict an early universe that doesn't match the observations and then have to start over, or if you think it's better to start from the distant past and work toward the now only to find a problem and having to start over.
But this is only true if they are the right equations.
If you look at an existing phenomenon that maybe relativity doesn't describe well enough, and find some modification to these equations that explains it better; and then you go and check that indeed this new model explains all known observations better - you have a pretty solid new theory. You can then expand this theory into the early universe and see what consequences it would have for the inflation model.
However, if you start from the big bang and want to modify Einstein's equations, what will guide you to a better model? Most likely you will use your intuition on how the universe must have begun - but then, chances are, your modified laws will predict entirely the wrong thing about the current universe; or, you can add terms to the existing equations that have no influence in the current universe, but then, by Occam's razor, your theory should just be discarded since it explains all observable phenomena equally well, but is more complex.
To be very clear this also happens when you start with a theory that describes the local universe well, indeed the fact that when general relativity extrapolated backwards gives blatantly unphysical results is the entire issue we are trying to solve!
Sure, but you have to start from observations of the binary merger, not from what you'd like the Big Bang to be like, like most of these theories do. Starting from predictions about the origin of the universe is unlikely to produce good testable theories, since there is nothing to test there. You have to look at phenomena that are actually still happening in the universe to guide your research, and only then extrapolate.