Allow me to attempt a dissenting opinion.
While I agree generally with all of the above observations, and find such arguments generally annoying, they can have a certain rational force in certain circumstances, and I am wondering why.
First, we have two "very dumb" (pardon the technical term) interlocutors, In1 and In2 and one belief (B1). The first interlocutor proposes only B1 for both In1 and In2. The second interlocutor proposes, let's assume, a second belief B2. We now have two interlocutors and two beliefs B1 + B2 with, mutatis mutandis, equal likelihood.
Now In2 proposes B1 + B2 - B1 = B2. She has effectively doubled the number of possible beliefs and then negated one. Even if she gives no good reason, In1 now has 50% less reason to believe only B1. In information terms, the number of possibilities to be rationally reduced to "certainty" has doubled.
Moreover, In2 has implied that there is some blackbox "reason" for B2, assuming they are two agents "reasoning" with one another. She implies that new evidence arose as time passed. By the principle of sufficient reason, there should indeed be some "reason" for the appearance of the new belief B2. Since In1 and In2 are already "reasoning," there is a non-negligible chance that she may have some "valid reason" for the new B2.
Nor is the matter of "trust" negligible or necessarily a rhetorical device. That "reason" too is unknown. But since both In1 and In2 shared B1 prior to B2, there is evidently some overlap of what they accept as "valid reasons." Hence a greater likelihood that the blackboxed "reason" may be valid.
In reality, this type of underwhelming argument does work best the more information and "possible beliefs" are limited, with "young" people, say, or people with "less expertise." Hence my qualification of "very dumb" and my limitation to just two possible beliefs between equally "reasonable" people.
In practice, the argument will carry scant weight in a world of infinitely many possible beliefs. We indeed quickly "grow out" of such arguments. But even where the "reason" is not given, good or bad, there is some probabilistic weight to the argument given very restricted beliefs. It is a bit like the Monty Hall paradox. All else equal (as it never is) In1 will technically improve odds in the new domain by switching to B2.