There might be something more in it than the commercial side seeing an opportunity for some free publicity (though this can't be ignored; if you want to get a book published anything that makes you visible is a help).
No, I'm not suggesting genetic tendency towards writing talent, or anything so esoteric, merely that if son has grown up watching daddy (or mummy, for that matter) typing away hour after hour, he starts with a clear concept of the work involved, and is not discouraged when it's not finished in a week; and a household which regularly uses a wide vocabulary and accurate grammar gives a better foundation than a simple scool education.
Doesn't mean it'll work every time, of course, or even a majority of the time; but evolution demonstrates, even the tiniest of advantages is not to be sneezed at.
There are few sons who have followed their fathers into writing careers and have been anywhere near as good. Offhand, in fact, I can't think of any (Martin Amis may have been as successful as his father, but as "good" as ...?)
Ian-I can think of one, a daughter though, Alice Sheldon wrote under the male pseudonym James Triptree Jr. to avoid being linked to her mother Mary Hastings Bradley; who was a noted literary and travel writer. I would say she was a much better writer in comparison and her works will be around for a very long time. The James Tiptree Jr. Award is given out each year to books that explore and bring greater understanding to gender in literature.
"Part adventure, part comic opera, and part geek nirvana, THE WAGES OF GONZO LUBITSCH is a story of love, pirates, politics, and apocalypses. It is set in a world not far from today and utterly recognisable. The Jorgmund Pipe, the backbone of the world and the only thing keeping the Livable Zone safe from the unreal world, is on fire. Gonzo Lubitsch, professional hero and troubleshooter, is hired to put out the flames – but there’s more to the fire, and the Pipe itself, than meets the eye. The job will take Gonzo and his unnamed sidekick - his chronicler and best friend since childhood – back to their own beginnings and into the dark heart of the Jorgmund Company itself."
However apart from the obvious post-nuclear setting it remains to be seen if he's a genre writer.
Anne McCaffrey has handed over the reins of Pern to his son Todd McCaffrey, who wrote some military fiction under his birth name Todd Johnson. I haven't managed to force myself into reading his books yet, but by and large they're panned in fandom (mainly because he has many of the failings of his mother, but none of the gifts which make her such an engaging writer in spite of her faults).