Sure, I wouldn't dare advocate the Cyrillic alphabet for English. But for Polish, which is a West Slavonic language and thus not a million miles away from Russian, it would be a great step in the right direction - indeed the right tool for the job! Actually, proposals were made to change to Cyrillic in the 1850s... the reason it never happened are myriad, but mainly Political. Which is also why it'll never happen! Poles are none to fond of their neighbours, for much the same reasons as Moldovans if I can hazard a guess. It's a real shame, because szsz is the classic case in point, it's really just one letter... and that's what you'd get with Cyrillic, namely a (and /. won't allow it, but the W with a tail, which no Russian would have a problem pronouncing)
Anyway, the adoption of the Latin alphabet in Poland is most likely due to the hegemony of the Roman Catholic church and the prevalence of Latin in the early church. Indeed, nothing much has changed in that respect. Every town in Poland worth it's salt has at least one street, school or square named Jan Pawel II... Polish is also a bit of an oddity, because whereas most Slavic languages using the Latin alphabet picked up the Czech orthographic system, Polish orthography developed independently.
By the way, if you speak Russian, Polish should be reasonably easy to pick up once you get past the orthography and learn to gadac[talk]. After all, spell piwo however you like, the best thing to do is still to drink it :)