This is completely wrong.
Gender is arbitrary only on the few monosyllabic suffixless words, that cannot be decomposed according to etymology.
Those words are not very numerous, there must be a few thousands of them, and they are the easiest words to know. (They are the words that mean simple things like "cat", dog, horse, book, case...)
This is not a problem. difficult words, words that you have never heard are NEVER impossible to decompose, they always have a suffix or a recognisable building pattern that makes their gender automatic, even if you do not know what the word means.
Contrarily to what you believe, the gender of the majority of the German nouns CAN be guessed, but the rules to do so are not easy to explain, (although they are built in the brains of the Germans), and they are rarely taught to English learners. in order to not frighten them.
I think that genders are as puzzling to an English speaker as the stress pattern is puzzling to a French speaker.
I have often (naively) wondered how it is possible for an English speaker to remember which syllable is stressed in every word they know, and often, in a word they do not know...
Contrarily to what I believed, the stress pattern of the majority of the English words CAN be guessed, but the rules to do so are not easy to explain, (although they are built in the brains of the English), and they are rarely taught to French learners, in order to not frighten them. (Which is silly, because not explaining something difficult does not make it easy, it makes it impossible, which is worse...)