Is it honest for authors to put the parents' names as co-authors on books - when the child did the writing and the parent may be dead?

It’s effective marketing, and not strictly dishonest, because the parent did the world/character building. As long as the actual writer is listed, it’s not dishonest.
James Patterson has a stable of writers that he hands off ideas to. He gets an author’s credit and either a royalty percentage, or all of it and pays the actual writers a wage (not sure how that works in his case, it’s probably researchable).

As long as all this is known, it may be a bit misleading if you don’t understand the system. This stuff is pretty obvious, and talked about.

ETA. And come to think of it, it has been posited that Mary Francis really did most of the writing for her husband, but because he had the marketable name, he took credit.

I think the same type of thing happened with V. C. Andrews of the Flowers in the Attic series. I think she has been dead for decades, but someone is still writing under that name.

I think if the quality is the same or at least as good, it doesn’t matter who wrote it. Series sometimes get picked up by other authors and I don’t necessarily hate it unless they change the characters of the people drastically or erase other characters that helped to mold the main characters, character.

Incomplete information. It depends.

Nothing wrong with using pen names. It’s when all of these talentless “celebrities” use ghostwriters that irks me.

Of course most celebrities use ghost writers, they are usually not writers. Ghostwriting is an old and honored profession, and I haven’t seen a celebrity memoir that doesn’t give appropriate credit where due.

I dont think the OP is referring to either ghost writers or pen names but to featuring the dead parent’s name who originated the series when the sequel is written by a child of theirs. I think titling it something like Lee Child’s Jack Reacher #12 as written by Andrew Child would be more ethical.

I’m not going to be uncomfortable with it if it’s family.

@janbb thanks for making it clear.

The Lee Child example is particularly interesting. I heard him interviewed (his real name is James Dover Grant) – he said a couple of things of interest:

1) that he didn’t like Jack Reacher – he wrote about him, but he didn’t like the character

and

2) that he was bored writing Reacher novels and was going to quit whether or not his son took over.

I’m fine with both of those comments; but then it seems inconsistent for him to keep his name on the cover.

By the way, if you compare the last couple Lee Child books (that HE wrote) to the early ones, the writing is notably different. Much more violent, plots are less subtle, and other characters not as well rounded. So I think he telegraphed his boredom by his writing.