So how can splitting improve the plot and story, eh?
Massively, indeed, simply because you can write good stories and don't have to bend everything so that every girls fits into the harem eventually. That's fine with 2 or 3 characters (maybe 4 to 5) but as soon as it's more than that the game usually suffers or gets boring pretty quickly.
Just take Mia's story as an example, where you've got Helen and Yumi. A split enables us to get a nice and somewhat meaningful story for Helen and Yumi each, because Harold will get the other one. It's the same with let's say June and Mrs. Johnson or Judith and the Latinas.
To a degree it's just as Eve's story would have benefitted from a "naughty branch", where MC doesn't go down the romance path but focusses more on the lewd stuff including Grace and Odette, so we could be spared the fact, that Grace has concerns about fucking MC and that there's no way to get her scenes without that.
Need to save and replay the game again?
The game tells you when to save and you can just start from there and play the other arc. I don't see the problem.
I personally think it's better to have one coherent plot and all the scenes concentrated in one playthrough, rather than "smeared" along many lines.
I personally think the opposite. Especially because the plot my be coherent but usually just becomes pretty meaningless.
After all, the STS was never advertised as an RPG game.
It was and is indeed advertised as "dating sim/VN" and as thus it's pretty reasonable to expect choices. In fact it would be odd if there weren't any.
Although it is possible to implement a "harem version" in the sitcom genre
To be fair, the game was never really meant to be a harem. Yes, you'd always be able to fuck every girl in town (it was never promised that it would be possible in one playthrough) but in the first ~18 months DC actually refused to even add a harem feature and only agreed because so many people wanted it.
I don't really know where the expectation that every girl should be fuckable in one playthrough comes from.