Perhaps the amount of different s sounds in Polish is too much for Cyrillic (a.o. historical reasons).
The reason is actually pretty simple. Polish, among other western Slavic languages, got fixed to writing by Catholic missionaries, who used the Roman script. All those Slavic languages using the Cyrillic script in past and present were fixed by Orthodox missionaries, who developed the Cyrillic script specifically for this purpose of being able to write the Bible in what is now called Old Church Slavonic, but is historically a predecessor of modern Bulgarian. One of the large historical differences between Catholicism and Orthodoxy is that Orthodoxy had no qualms about using local languages for liturgy. That's why there are distinctly Greek, Bulgarian and Russian Orthodox churches, who all had their own translations of the Bible and used their languages in church.The Catholics on the other hand were adamant about using Latin until a rabid antisemite called Martin Luther came about, and Catholicism has always been much stronger bonded to Rome (Latin) than Orthodoxy ever was to Constantinople (Greek).