Historical Necessity
Bit slicing (although it was not called that) was also used in computers before integrated circuits. The first bit-sliced machine was EDSAC 2, built at the University of Cambridge Mathematical Laboratory in 1956-8.
Before the era of modern computers (mid-1970s through late 1980s) there was some debate over how much bus width was necessary in a given computer system to make it function. Silicon chip technology and parts were generally much more expensive than today. Using multiple simpler (and cheaper) ALUs was seen as a way to increase computing power in a cost effective manner. 32-bit architectures were being discussed but few were in production.
At the time 16-bit processors were common but expensive, and 8-bit processors, such as the Z80, were widely used in the nascent home computer market.
Combining components to produce bit slice products allowed engineers and students to create more powerful and complex computers at a more reasonable cost, using off-the-shelf components that could be custom-configured. The complexities of creating a new computer architecture were greatly reduced when the details of the ALU were already specified (and debugged).
The main advantage in the late 60's to mid 80's was that bit slicing made it economically possible in smaller processors to use bipolar transistors, which switch much faster than NMOS or CMOS transistors. This allowed for much higher clockrates, for applications where speed was needed; for example DSP functions or matrix transformation, or as in the Xerox Alto, the combination of flexibility and speed, before discrete CPUs were able to deliver that.
Read more about this topic: Bit Slicing
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