If the kid didn't disappear, the player could, theoretically, have a child with EVERY bachelor
and bachelorette in one file (and this is before the DLC bachelor/ettes arrive.) This would lead to a programming nightmare for a multitude of reasons, and they'd have to dedicate a large swathe of time and money into just this one feature. I also think saying 'kill' the kid is a bit dramatic, when it's a rewind feature at best. That article is being extremely clickbait-y.
Personally, I would've just not included a divorce/rewind feature, but I understand its inclusion; in case you marry somebody and aren't happy with them, being the main reason I assume.
I also just personally take umbrage with game devs being called 'lazy' in general. I've seen what 'lazy' games look like, and Olive Town isn't one of them, warts and all. I think it's easy to accuse game devs of being lazy when they take the simplest route to a solution, and it's easy to say 'well, they could've done this, that, and the other thing, like this other game did' without actually knowing the logistics of how feasible that actually is for that particular project (Olive Town, in this case). Sure, I think the child being deleted is pretty strange, personally, but I also don't have any ideas for how they realistically could've done it alongside including the rewind feature.
I think this forum as well as most gamers in general would do well with checking out
Ask A Game Dev on tumblr, who has a lot of interesting insight into how games get made on the professional level. Maybe somebody here could ask about Olive Town, if they were so inclined.