I agree that 'they/them/their' is and has been for a good long time a grammatical and reasonable [more reasonable than 'his'] use with grammatically singular but notionally plural pronouns.
The 'his' alternative was an artificial construct that was meant to try to stop what was a natural language use. What's worse, it attempted to end the use of 'they/them/their' based on a misconception about English pronouns.
Grammar Puss
...
Sometimes an alleged grammatical
"error" is logical not only in the
sense of "rational," but in the sense
of respecting distinctions made by
the logician. Consider this alleged
barbarism: Everyone returned to
their seats. If anyone calls,
tell them I can't come to the phone.
No one should have to sell their home
to pay for medical care.
The mavens explain: [everyone] means
[every one], a singular subject, which
may not serve as the antecedent of a
plural pronoun like [them] later
in the sentence. "Everyone returned
to [his] seat," they insist. "If
anyone calls, tell [him] I can't come
to the phone." If you were the
target of these lessons, you
might be getting a bit
uncomfortable. [Everyone returned
to his seat] makes it sound like
Bruce Springsteen was discovered
during intermission to be in the
audience, and everyone rushed back
and converged on his seat to await an
autograph. If there is a good chance
that a caller may be female, it is odd
to ask one's roommate to tell
[him] anything (even if you are not
among the people who get upset about
"sexist language"). Such feelings of
disquiet -- a red flag to any
serious linguist -- are well-founded.
The logical point that everyone but
the language mavens intuitively grasps
is that [everyone] and [they] are
not an antecedent and a pronoun
referring to the same person in the
world, which would force them to agree
in number. They are a "quantifier" and
a "bound variable," a different
logical relationship. [Everyone
returned to their seats] means "For
all X, X returned to X's seat." The
"X" is simply a placeholder that
keeps track of the roles that players
play across different relationships:
the X that comes back to a seat is the
same X that owns the seat that X
comes back to. The [their] there
does not, in fact, have plural
number, because it refers neither to
one thing nor to many things; it does
not refer at all.
On logical grounds, then, variables
are not the same thing as the
more familiar "referential" pronouns
that trigger agreement ([he] meaning
to some particular guy, [they]
meaning some particular bunch of
guys). Some languages are
considerate and offer their speakers
different words for referential
pronouns and for variables. But
English is stingy; a referential
pronoun must be drafted into service
to lend its name when a speaker needs
to use a variable. There is no
reason that the vernacular decision
to borrow [they, their, them] for the
task is any worse than the
prescriptivists' recommendation of
[he, him, his]. Indeed, [they] has
the advantage of embracing both sexes
and feeling right in a wider variety
of sentences.
http://pinker.wjh.harvard.edu/articles/media/1994_01_24_thenewrepublic.html