Still complex compared to Polish, which has a ratio of letters-to-phonemes much closer to 1 (five digraphs in total). While it's a hard language to learn overall, its orthography is one of the parts that are pretty simple compared to English. Only three homophone pairs are present throughout the language (H/CH, Ż/RZ, Ó/U); voicing and devoicing is a thing (PRZ... almost always sounds like PSZ...); Ą and Ę have a rule where they are fully nasalized depending on context; palatalization is everywhere, and it's probably the most complex part. Foreign words are very often polonized ("onomatopeja" from your example).
Maybe I'm biased as a Polish native but I do not think the above is comparable to the mess of exceptions that is English.
A phonetic script is one where the symbols represent sounds. The Latin alphabet is a phonetic script. In contrast, consider the shared numeric system used in both English and Polish. How do you pronounce "1"? What about "10" or "11" - does using the same symbol in all three numbers give you any hint about whether they sound the same? What if I'm saying the numbers in French?
The answer is of course, no, those symbols don't have an associated sound. They have an associated meaning and there are many spoken words for that meaning.
Maybe I'm biased as a Polish native but I do not think the above is comparable to the mess of exceptions that is English.