This is a topic I've thought about a lot myself in the past. And where I come down is that it IS a conceit of a lot of shipfic where making the ship believable/understandable to the "layman" is secondary to or simply not a factor in the story that the writer is telling. But my reaction to that is not to feel like this fic is inherently lesser because of it, but rather to understand who it's being written for and why.

It is, I agree, completely valid to want to write established relationship fic or shipfic that is about a whole bunch of other things besides How These Two Got Together. And a major reason that these fics, many of which I've written myself, don't bother with the burden of proof or whatever is because the audience is often people who already want to read this. If I'm writing a ship about X/Y who aren't involved in the canon, I'm not necessarily writing this in order to explain to every random passerby every single thing that made me see the potential for this relationship in the canon. I'm writing it because there's something I want to explore here and, like you said, I'm going to hope that my portrayal of the characters and the relationship I construct is well done enough to make good sense. In some cases, hopefully it will also giving a sense of what I see in it in the canon. But if it doesn't, no big deal. As long as it makes internal sense as a piece of writing, I haven't failed at anything.