What you imagined "投了错险" is grammatically right and be able to be understand by every Chinese.
But "投错了险" is the form spoken by us Chinese everyday. It is nothing to do with your understanding of each word's role, but just word turn.
And obviously, you translated "take out the wrong insurance" word by word, turn by turn. That's the reason why you think it should be translated like "投了错险".
You cannot translate the sentence form a language to an other language word by word, turn by turn. Each language has its word turn.
In fact, at the time that written Chinese and spoken Chinese are using different grammar (it's not much long time ago, just about 100 years), "投错险" would be a wildly received form in written Chinese (though there were no insurance industry in China at that time). And literally, it means "take out the wrong insurance".
"投了错的险" is also grammatically right but little hard to be understood. And the best form is "投了错的保险". In the phrase "投了错的险", "险" might be thought of "dangerous" firstly because the verb "投" is too far away from it, and people might be not able to connect the verb "投" with the noun "险" immediately.
"投错" is a phrase which means "take the wrong ..." at the most time, but not a word.
Plus. It don't think a Japanese would confuse "银行" and "很行". Because "bank" in Japanese also is "銀行" -- the same to Chinese -- just written in traditional Chinese characters.