A few of us luthiers out on the wacko end have made basses with this style of pickups, using a separate coil for each string. Here's the "M-Pickup" that I developed for one of my Scroll Bass models a few years back.
Each coil has three 1/4" Alnico 5 rod magnets. The four coils are wired together in series, but with alternating wind directions and magnet polarities. So the group functions as a humbucker.
The main reason I developed this pickup is because this model bass has a 4" fingerboard radius. I needed the independently adjustable coils to get an equal output from the four strings. But a side effect of this configuration is a "sensing aperture" that's the opposite of most pickups. The aperture is quite long along the length of the string, and narrow across the string. The result is an increase in the dynamics and attack profile, from plucking, and a reduction in harmonics and ringing.
It's a great sounding pickup with flatwounds on that style of bass. I also sold one set to a player who used it to electrify an upright, and they worked very well for that. But I tried a set in a conventional electric bass with roundwounds, and the owner didn't like them. I think they didn't have enough high end for his taste. That may just have been the particular formula that I wound those coils to.
Anyway, there's plenty of room for experimentation with multi-coil pickups. I don't think there are any massive advantages to them, but they can allow some unusual configurations. Not many companies have used them in production instruments, because they are expensive to build. Squeezing pickups into small packages is extra work. I had to make up all of my own bobbins and parts for these.