Do you object to the fact that the spelling "th" invariably means /þ/ or /ð/, and not /th/? Or mapping "sh" to /ʃ/ and not /sh/? I highly doubt you do.
Here's the thing: spelling rules are context-sensitive, and if you actually understand the underlying sound rules, spelling in English is often not that bad. For example, there is a fricatization process for /t/ and /s/ sounds convert to a /ʃ/ or a /ʒ/--this is how "-tion" is pronounced /ʃən/. Or the tendency of multiple consonants in a cluster to all be voiced or unvoiced (hence why dogs is pronounced /dogz/ and not /dogs/). Even consider the velarization of "n" in the "-ing" suffix, which is pronunced /ŋg/ and not /ng/ (try actually pronouncing /ng/! It's not easy).
I'm not aware of any spelling reforms that would propose to fix the last two examples I give, but the fricatization changes is often one of most common ones people suggest changing. That's a sign that people are willing to tolerate some degree of phonetic inaccuracies.
The real issue with English is our tendency to adopt foreign words with foreign pronunciations, foreign spellings, and sometimes even foreign morphology. And sometimes we even botch that--witness words like "gyro" or "ginkgo". This means that trying to pronounce unusual words often means first guessing what language the words (or even morphemes!) comes from, and then internalizing some bastardized form of that foreign language's phonology.