I think rz is linguistically equivalent to a soft r, so in this case rze would be "ре", not "ж". In some areas, rz is pronounced closer to the Czech ř. IIRC, ж transliterates to ż (not to be confused with ź, which is a soft z). The Polish Roman alphabet is very regular and well adapted to the language, representing palatalization and other non-Latin sounds as digraphs in a similar way to Italian or English.

The cyrillicization of Polish was historically done to a limited extent, but carried with it some, shall we say, sociopolitical baggage. There are also some peculiarities to Polish that either don't exist or have ambiguous transliterations into Cyrillic, such as the Polish nasals ą and ę or ó (historically a long o, but currenly pronouned /u/).