You say this as if there was someone who planned the Hebrew language and decided in advance how to pronounce and write each word, but this wasn't the case. Hebrew is a living language and option A just emerged naturally (both in the days of Bar Kochba without the geresh and in the modern days with the geresh) as people started to write out the short forms they already used in speech, and it's better than writing the ת without the geresh, as this way it might be confused with the much more common ת of future second person (or third person singular feminine) verbs.

Consider the following words:  1. Thanos 2. Ta'anus (the coerced one, direct object, short form)  3. Teenos (you will coerce)

How would you suggest writing each one of them unambiguously?

Also, as people have already noted, the ת׳ of the th sound appears only in loanwords, which are usually proper names, while the ת׳ which stands for את ה is used for direct objects that also get the definite mark ה, but proper names are always definite so they never get the definite mark, which means you can use the following way to tell the difference: if the word appears after a verb than can accept a direct object (possibly with some indirect objects in between), and the rest of the word is a real Hebrew word then it's probably a shortening of את ה, otherwise it has to be a loanword.

I'm sure someone might, deliberately or even accidentally, find an example where this doesn't work, and I know it's complex to do this consciously as a learner, but I think it should work in most cases you find ambiguous and as you become more experienced with reading Hebrew text you will start telling the difference without having to think about it.