Dear Vladimir Rogozhin,
thanks a lot for pointing me to this very interesting open letter. Indeed, cosmology is one of the most model-dependent theories we have due to sparsity of data obtainable and the lack of experiments we can perform (except for some analogues in lab experiments, we have to rely on serendipitous discoveries), among others. Yet, it is no unique phenomenon that one "mainstream theory/model" has been developed and others fell out of focus, this is not much different from other highly complex sciences, e.g. medicine.
This trend to favour a particular idea and abandon others completely was a major motivation to write my essay. In my view, running in a single direction and adjusting inconsistencies with further assumptions even if we keep on lacking observational confirmation makes us blind for alternative models compatible with a sparse set of data.
Underdetermination problems allow for a variety of solutions and we should explore the set of all of them (including ambiguities in the representation of each model solution). As Richard Feynman once said so pointingly in his famous lectures at Cornell, up to a certain level, many different interpretations / descriptions of a phenomenon are possible but not all of them inspire us equally well to move to the next level of a deeper understanding. While it may be a costly and dry task to systematically investigate develop a complete model to explain all cosmological data, we are much more likely to find those solutions that inspire us to a deeper understanding.
Personally, I find that the big-bang theory is a good example for a highly sophisticated abductive model discussed in my essay and I agree to the criticism put forward in that open letter, not necessarily because the big-bang-theory may be incomplete or wrong but because I would like to know whether this is the only solution currently compatible with our data. As far as I know there are also other models that have not been rejected based on observational evidence so far.
Another criticism I would have, is that there have been arguments from philosophy of science that the big-bang theory can hardly be refuted due to its construction. So one may also ask in how far this model is a dead end if our technology will not give us any observational confirmation nor is there any self-inconsistency in the theoretical framework to refute the idea on deductive grounds.
Best wishes,
Beige Bandicoot.