I agree with the thrust of your comment that vernacular is what it is and attempts to police it are foolish. Though there's no need to be rude. And "he" is not
a vernacular (Muphry's Law?). But this case is a lot more subtle than you imply.
Generic singular "he" is an older usage that is slowly phasing out as society changes. When I find myself using "he" for this, I always notice that it doesn't quite feel right anymore. Of course most people who favor this usage point to its "standard" correctness (cf. this thread), but that's pointing to the past. What's interesting is that we're in a pluralistic stage where there are many competing alternatives -- generic "he", alternating "he" and "she", "he or she", singular "they" -- none of which quite feels right.
This is untenable in the long run because it forces you to think about which one to use. That's way too much runtime overhead, and it's not how language works. Vernacular is a don't-make-me-think thing. That's the real problem with sprout's suggestion in the GP, i.e. rewording to drop the generic singular altogether. It's a viable alternative, and I do it all the time, but it's also the most expensive.
There's no way this gap won't get filled. The only reason we haven't seen it yet is that fundamental language shifts are slow relative to a human lifespan.
The option I find most annoying is the "sometimes use 'he' and sometimes use 'she'" one, which is like solving a design problem in a function by offloading it entirely to the caller. Not only do you have to think about which one to use, you also have to reference-count to keep the two in balance over time. No way is that one going to survive. (I also find that people who do this tend to be annoying tsk-tsk types, though maybe that's a prejudice.) My money's on singular "they", because it's the simplest, it's truly generic, and -- amusingly contrary to all the pseudo-grammarians who freak out about it -- it has a long history in English. Great examples at http://en.wikipedia.org/wiki/Singular_they.