We can't make the C string like the others (2 covers over a round core) so it wouldn't be "balanced" in that regard. However, moving from a 2 cover G string to a 1 cover C string isn't that drastic of a tonal difference, oddly. I've been using a 6st set of Round Core Bass Boomers (which have the same construction as BN now), and it's fine.
So, if we did make a BN C string, it would be along those lines. However, people simply haven't asked for one. The demand for a 6 string set is small already (compared to 4 or 5 string sets), and I can count on one hand how many times people have specifically requested it.
It's still possible, but realistically I wouldn't count on it.