Not only is they the obvious alternative, it's always been perfectly good English and has been traced back to long before generic he was introduced—by Latinists who wanted to make English more proper in I forget which century. Now that generic he is rightly getting dumped, the natural solution that existed all along—singular they—is making a comeback. It's a lot better than stilted fabrications like "he or she", "s/he", and the hideous "ostentatious she" that some people (seemingly always liberal males) insist on using to denote programmers, venture capitalists, and other demographically lopsided populations—as if changing the ratio of pronouns would change the ratio of people.

The fascinating thing is that generic he was an ideological construct in the first place, a top-down imposition that never fully caught on in English despite literally centuries of being proclaimed as proper. Singular they continued to be used the whole time, and is found in most (all?) great English writers. (Jane Austen was particularly fond of it.) I don't have citations handy, but people with similar bees in their bonnets have made sure that web searches won't lack for them.

This is something that I always saw as 'English syntactic sugar' as a non-native speaker.

When I realized that a plural form of the third person could be used in a gender-neutral way for the singular form, I was in awe.

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Trivia:

In French, the common rule is "le masculin l'emporte"[1], which means the "male form wins"; if you talk about a group of 100 females and a single male, you must use the male form "ils" instead of the female form "elles".

[1]: [...] on abrège parfois cette règle en "le masculin l'emporte sur le féminin", alors qu'il serait correct de dire : seul les groupes exclusivement féminin sont féminins, les autres utilisent le genre non marqué.

Roughly translated to : It is more correct to say that groups exclusively composed of females are accorded using the female form, while the other groups use the 'unmarked' form (which is the male form).

I usually use they, but now that I think about it, I'm going to start using s/he. It's the same number of characters as they and you can just pronounce it like she when reading it aloud or in your head, since she is the underused pronoun anyway.