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.
Why would we? It "just works". We've only changed how we write the letter "ż" some 30-20 years ago. It was previously "ƶ". Also, "ż" and "ź" are not accents but separate alphabet letters.
There was no typeface change for “ż” - the other typeface is sometimes used now as it was 30 years ago. See the foto at Wikipedia: https://en.m.wikipedia.org/wiki/%C5%BB
And yet, you can see the "Straƶ Miejska" logotype linked in my comment above, with a crown on the eagle, so post-December 31, 1989[0].
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.
You could also look at Croatian, which has a similar contrast with e.g. "C", so they use "č" and "ć". This could be easily extended to "s" and "z". Or you could take "ż" and apply the same diacritic to "c" and "s".
"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.
At this point it’s a unique aspect of the language, so much so that changing sz to š for example would feel like a betrayal. There are also a few letters without similar sounds in other Slavic languages (ą and ę) so you’d end up retaining those anyway.
Those make sense since they aren't digraphs. But c'mon, comparing Czech to Polish, it's pretty clear which orthography was designed first, and which learned from the mistakes of the other :)