At one time viscous coupling units were one of the key factors in the development of all-wheel drive systems, allowing them to be introduced into on-road vehicles.
The torque (M) transmitted by the viscous coupling unit is sensitive to the difference in speeds of the input and output (Δn) and to the temperature (υ).

(some viscous coupling unit)
So the application of the coupling in all-wheel drive has been a two-way thing. In the more advanced case, it was used in conjunction with a conventional (inter-axle) differential to lock it automatically. In the more budget-friendly case, the viscous coupling was a substitute for the inter-axle differential, allowing the second axle to be engaged on-demand.
Applications in conjunction with the differential were found in both on-road and
off-road vehicles. The application as a differential replacement is more the domain of relatively inexpensive, but still all-wheel-drive road cars.
It is interesting that the first generation Jeep Grand Cherokee (ZJ) had
both options: first (1993-1995) the viscous coupling was used in Quadra-Trac system as automatic locking of differential, and then (1996-1998) the viscous coupling was used to engage the front axle on-demand. And it turned out to be "the complete opposite". The first version of the system was more suitable for the roads (because of the lack of manual inter-axle differential lock, viscous coupling can not ensure it), and the second one for off-road (because of the presence of a forced lock, if you do not forget to activate it by switching to 4Lo).
It is also possible to remember the four-wheel drive systems of other manufacturers as well.
There were also some odd experiments. For example,
Honda INTRAC (1988-1995) used two viscous couplings in the rear axle, which both replaced the rear and inter-axle differentials.
Then it was clear that viscous couplings would become obsolete, despite their simplicity. They had many drawbacks: lack of control, slow, even unpredictable operation, a tendency to overheat, and low reliability.
There were attempts to replace the viscous coupling with an automatic hydraulic control clutch: for example,
Honda Dual Pump, and
Quadra-Trac II/Quadra-Drive on the second generation Jeep Grand Cherokee (WJ/WG). However, it was not further developed.
As expected the electronically controlled coupling has won. It is the basis of the majority of modern four-wheel drive systems, up to extremely exotic implementations such as
Active Drive 2/Active Drive Lock on Jeep Cherokee (KL).
But the viscous coupling continues to be used in all-wheel drive systems. These are mostly cheap JDM cars where economy is important (Kei cars and so on), but the presence of all-wheel drive is significant.
Suzuki, for example, still uses them today.

But I was more surprised that such a system of all-wheel drive is used in the current Honda Fit, including a rather advanced
e:hev version.

But, of course, in some situations, it is better to have all-wheel drive with a viscous coupling than just two-wheel drive.