Gendered nouns and pronouns are the bane of language. Arbitrary grammatical gender/noun class is stupid. Case would more than suffice and is easier to handle as language evolves.
Why is that, exactly?
You're going to have to excuse me. This is going to be disjointed and not at all elegant. I'm at work and don't have the time to write a ten page post on applied sociolinguistics. I'm reasonably sure that neither you nor anyone else on BSN wants to read one.
Operating terms:
Pronoun: A short hand way of referencing a previously mentioned or implicit noun and its associated adjectives and determiners.
Case: Changing the form of a word based things like whether it's the subject or object, its plurality and so on. Example: I/me/we/us
Gender: An arbitrary way of classifying nouns, used as a way to lessen potential ambiguity. Gender is present in an estimated 30% of the world's languages, which can have anywhere from 2 to 10 genders. Example: masculine/feminine/animate/inanimate/neuter
Now to the problem: Gender is, as I said, completely arbitrary. It varies from one language to another and is often inconsistent within a given language. It frequently makes no sense at all. Why is a city feminine or a river masculine? Why is that completely opposite in a different language? A cat is animate, but is a dead cat inanimate? In some languages, the word for "girl" is not feminine, but neuter or even masculine. Worst of all, grammatical gender has become conflated with natural gender (sex) when the two are completely different concepts that apply to completely different things. Just a few hundred years ago, gender didn't refer to sex at all.
Languages evolve and change over time becoming more complex in some areas and simpler in others, merging and separating both internally and externally. That's a good thing because the world is not a static place. However, remnants of old systems sometimes linger on and make things confusing and complicated when they don't need to be. English has pretty much abandoned both case and gender, but it still hangs on prominently in the case of pronouns. We still have case in the first-person, second-person and third-person plural. In the third-person singular we have both case and gender. As society moves on, so do linguistic concepts. In modern times, we find that we really don't need gender in English. As far back as the 1100's, the best writers realized this. Chaucer, Shakespeare and others were using "they" for third-person singular. However, the patriarchal institutions at the time wanted to cling to the older system and declared that "he" should be the gender-neutral pronoun.
This is getting really, really long, so I'll wrap up. Most English-speaking countries and institutions are coming around, officially encouraging the gender-nonspecific "they" for third-person singular, although it can still be confusing at times. A new case, a singular form of "they", would help a lot. "It" could have worked, but it's already tainted as gender-neuter/inanimate. The best solution would probably be obviation. An example would be use two different third-person singular pronouns to indicate relative salience of the two objects. Here's a really bad, clumsy example:
Tim: "Bobby and I were going to fight after school. A big crowd gathered to watch."
John: "What happened?"
Tim: "It turns out that they-1(Bobby/he) chickened out and they-2(the crowd/them) started making fun of they-1(Bobby/him)." The latter could also be "they-3", if we retain the use of case.
I really need to get back to work, but I hope that helps.