It is a weird speed, but then again so was TXP, at 320, vs TriX at 400. My guess is that it was as fast as the first guy marketing something faster than 100 for portraits could stand to make and still bill it as for portrait use. Then the rest followed suit.
It is not just the low contrast ones, but others of the pro film lines as well. Fuji NPC and NPS, now called 160 something (I don't recall), Kodak Portra VC, and NC.
Ektachrome tungsten balanced E-6 used to go 64 than 160 then 320 too.
They have been increasing the speed of the C-41 portrait films through the years, they started at 80, then 100, then 125, and now 160. Since they are widely used in 120, 220, and sheet sizes, thus typically with slow lenses, users appreciate every additional third-stop of speed.
I kind of wonder why we have stopped at iso160 then. There are 400 iso versions, but is iso 200 too close to iso 400? Is the speed kept at 160 to differentiate them from 200 iso consumer films? Did digital come along and begin to kill the portrait film market before a 200 iso version emerged?
Well there have been additional technology updates, like 2-electron sensitization. These films could be ISO 250 or ISO 320 or something like that, but instead they have made them finer-grained. That is wise, because we already have ISO 400 versions (with the same technology upgrades, so they could be 640 or 800, but we already have ISO 800... etc .
And this might be a hunch, but ISO 160 can be pretty fast in good sunny light when you use a camera with a top shutter speed of 1/500th or 1/1000th, which a lot of medium formay cameras are limited to. E.g. my Autocord goes up to 1/500th and with ISO 400 in there in good daylight, you're shooting at small apertures generally.
There again, I have never struggled to use ISO 64 in variable light.
So anything much faster than 160 I'd become creatively limited in some light as to what aperture I can use on MF cameras, and my M2 and OM2n.
And isn't amazing that many film's sensitivity (a thing that does not know about our liking for nice, rounded whole numbers) happens to conform to our neatly ordered and organized 100, 200, 400, 800, scheme?
Where are all those 562, 193, 378, 283 etc. ISO emulsions?
A better question, why don't film speeds have the same numbers as shutter speeds? Sunny-16 would be a lot more convenient if shutter speeds went 50, 100, 200....
Coming from a 'oldtimer' perspective in wedding photography, 160 was the standard film speed, and most rated VPS at 125 for a bit more shadow detail. The 160 was really handy when you had to calculate Guide Numbers on the fly with a non-Auto Norman 200b, but after a while got easier, 10 ft is f16. I still find that speed capable when doing outdoor bright light portraits with fill flash, 1/250 and f11 for a decent distance works well. I wish my D3 went lower, I guess I'm the only one who has to shoot in bright light on a beach with flash at something less than F32.