The 'rz' phoneme has the same sound as the letter 'ż' which is a different sound from the letter 'ź' (the latter being a softer sound - one that foreigners usually find easier to reproduce).
Whether you write a word with the 'rz' or the 'ż' is governed by a set of orthographic rules that are of course peppered with numerous exceptions.
> It represents the same sound in the Polish alphabet, remaining in active usage by some as an alternative for the letter Ż (called "Z with overdot").
> In Polish, the character Ƶ is used as an allographic variant of the letter ⟨Ż⟩ (called "Z with overdot") although once used in Old Polish.
Funnily, there's a counter-argument to "Straż Miejska" from article you linked, with "Straƶ Miejska" in another Wikipedia entry[1] :)
It may depend on the region (I was raised in the eastern Poland) but I also remember that in the primary school we used a different symbol for the letter "s". But only in hand-writing while any printed "s" looked like it does currently. I'm unable to find the UTF-8 character resembling the hand-written version.
sz contrast with ś/si, as does cz and ć/ci, or ż/rz and ź/zi, or dż and dź/dzi
(might have swapped one or two)
Add in some good etymological reasons why the consonant+i combinations are not respelled and the whole thing makes a lot of sense.
"rz" is a bit of a special case since it's pretty much etymological - what used to be "r", and corresponds to "r" in the same roots in other Slavic languages, but became to be pronounced like "ź" in Polish. What to do about it depends on whether you want your orthography to be purely phonemic (a better choice IMO, just look at South Slavic languages - it works great for them!) or retain the etymological distinction. But even then it would be better off as a diacritic.
What would be really neat tho is having a single Latin-based notation that works consistently across all Slavic languages, similar to https://en.wikipedia.org/wiki/Common_Turkic_alphabet. For example, we could use cedilla to represent post-alveolars: ç and ş - and then use acute accent to indicate palatalization ("softness"). So e.g in Czech you'd only need s/ş, in Polish you'd use s/ş/ş́, and in Russian you'd have all four possible combinations s/ś/ş/ş́.
Tiny correction: "rz" is spelled exactly like "ż", while "ź" sounds differently.