Any peer reviewed article which does not come at least with the reviews has only a social validation. With reviews which contain only value judgements, grammar corrections and impossible to validate assertions, there is not much more trust added.
As to the recourse to experts… what are we, a guild of wizards? It is true because somebody says some anonymous experts have been consulted and they say it’s right or wrong?
Would you take a pill based on the opinion of an anonymous expert that it cures your disease?
Would you fly in a plane whose flight characteristics have been validated by the hear-say of unaccountable anonymous experts?
What is more than laughable is that it seems that mathematics is the field with the most wizards, full of experts who are willingly exchanging private value opinions, but who are reluctant to make them in public.
Case by case, building on concrete examples, in an incremental manner, it is possible to write articles which can be validated by using the means they provide (and any other available), by anyone willing to do it.
It is time to renounce at this wizardry called peer review and to pass to a more rigorous approach.
Hard, but possible. Of course that the wizards will complain. After all they are in material conflict of interests, because they are both goalkeepers and arbiters, both in academic and editorial committees.
But again, why should we be happy with “it’s worthy of publication or not because I say so, but do not mention my name” when there is validation possible?
The wizardry costs money, directed to compliant students, produces no progress elsewhere than in the management metrics, kills or stalls research fields where the advance is made harder than it should because of the mediocrity of these high, but oh so shy in public experts who are where they are because in their young time the world was more welcoming with researchers.