Cyrillic really isn't any more phonetic than Latin. Use of Cyrillic/Latin script in Slavic languages is based more on religion than anything (look at the division in Serbo-Croat), and it's doubtful that predominantly Catholic Poland would have ever felt tempted to switch to a script devised by Orthodox monks. More likely, Polish could have used a system based on Czech spelling - ie cut out the awkward digraphs.
But these things rarely pan out in a logical manner, and we're now at the stage where too many people are literate in the current system to put up with the upheaval of a mass spelling reform.
As a native American English speaker learning both Russian and Polish, Cyrillic seems more phonetic than Latin to me, though I guess it depends which language you compare it to. Spanish is highly phonetic, but English and Polish are more strange.
In my experience so far, Polish seems pretty similar to Russian, so Cyrillic seems a pretty natural choice, assuming the same, straightforward phonics are kept (big assumption).
I can accept that it's not going to happen anytime soon, but I do think that if it could be done, Cyrillic would be easier for Polish.
I don't believe if we had cyrilic system it could be more phonetic. Russian still is not 100% phonetic. And those changes in language that made us have 2 letters for one sound would have happened. And we would still write ławka, with w instead of f. but one letter for szcz could makes typing faster.
I know Cyril and Methodius are Catholic saints, who developed one writing system (I can't recall its name.), and their pupils later developed Cyrillic and named it after Cyril. Were their pupils not Catholic?
There are several different kinds of Orthodox, and while some are separated from the Catholic Church by schism, others are fully Catholic. What type of Orthodox were Cyril's pupils?
the answer to your question is - it happened before the split between Greek and Roman church. Cyril and Methodius were Greek so their pupils mostly stayed on the Greek side of the dispute - Orthodox church.
they lived in 9th century and the split happened i 1054. https://en.wikipedia.org/wiki/Saints_Cyril_and_Methodius
The writing system is called "Glagolitic" in English and "Glagolitsa" in Croatian and other Slavic languages. (In Ukrainian, it's called "Глаголиця"- "Hlaholytsya"). "Hlaholyaty" (Ukr.) or "glagolijaty" (Old Church Slavonic) means 'to speak', 'to utter'.
Old Church Slavonic was used by both 'Catholic' ('Universal Faith') & 'Orthodox' ('True Faith') Byzantine Rite Christians. I hope this helps.
I expect the Polish nation would never accept an alphabet which they regard as Russian, having been under russian dictatorship for much of their history, they want to express their independence. Their language and alphabet are central to that. Those who speak russian that they were forced to learn at school in the 20th century, generally hate the language as it is a vestige of communist dictatorship.