I am purely talking about changing the spelling. The Fugen-S is something you actually pronounce, so if you want to keep the language intact and spelling phonetical, you would keep the Fugen-s.
Yes, it might be a bit weird to you. But it's no weirder than other changes we make to words in German because of grammar. Like 'kleiner Hund' vs 'kleine Katze'. Adding an 's' on the previous word is no worse than adding an 'r'.
It's actually not always clear. There are "Einkommensteuer" und "Einkommenssteuer" and you could write and pronounce them either way. Same for "Bahnhofstraße" and "Bahnhofsstraße". But yeah, I guess these are some rules that developed around the practice of writing words together.
It's also interesting when you split up the words. For instance "gebrandmarkt" results in "brand gemarkt". So you extract the "brand" from "ge-...markt".
Your corner cases are mostly about compounds where the next word starts with an s or sch sound. There's also selbständig vs selbstständig, where both variants exist with speakers of the language, and 'official' German picked first one and later the other variant as the 'official' one.
> It's also interesting when you split up the words. For instance "gebrandmarkt" results in "brand gemarkt". So you extract the "brand" from "ge-...markt".
You would probably write "Sommer Nacht Traum" instead. The fugen-S of "Nachtstraum" only makes sense, when you connect "Nacht" and "Traum".
(English has no fugen-S, as far as I'm aware)