Why is a chet with a patach at the end of a word pronounced "ACH" and not "CHA"? Example: מָשִׁיחַ
Actually, the question is why it is spelt differently, and not why it is pronounced differently at all. If you wanted to say meshicha, you certainly could. That would be a different word, of course, though a related one. It would be spelt משיחה.
For words that end in -ach, orthographic convention has us conclude them with the chet. This is also the case for words ending in -'a (such as רקיע) and in -ah, where the final ה is consonantal (such as אלוהּ).
The reason for all of these is that the final vowel/consonant combination is not preceded by a phonological alef, but by a rounding off of the previous vowel. Hence, mashi(y)ach, raqi(y)a and elo(w)ah.