Indeed, it's one of the peculiarities of the Polish language that it has Slavic phonetics but a Latin alphabet. Hence why typically Slavic phonemes, which in Cyrillic are represented by single letters (such as sh = ш), in Polish get represented with two (sz), and why you need a double-letter context to know how to pronounce a given sequence of characters.

Unfortunately, back in the 10th century, the choice of an alphabet was essentially a pure consequence of whom the first ruler of Poland would adopt Christianity from: the Western part of the Church (this was before the official Schism) or the Rus (Ruthenia). The Rus had a liturgy in Old Church Slavonic, and for the liturgical books they adopted an alphabet, the Glagolitic (a predecessor to the Cyrillic), which was more suitable for the phonetics of the language (and, indeed, of Slavic languages in general). Poland adopted the Latin liturgy and the alphabet was part of the “package”.

I blame it on Methodius. He tried to get the Catholics to use the Glagolitic but in the end it didn't take and the vacuum got filled with Latin.