Once filter design was mostly done by the analog filters. Even after the introduction of digital filters the design was not preferred due to the number of stages involved in the design. The need for memory to store the data(filter coefficients should be stored in digital filter design) made the design more costly.
So the design was only used where the cost was not a problem.
Later the digital filters made practical designs possible which are impractical and impossible by analog filters.Example: Audio Frequency Range.
At this range the practical filter design was thought to be impossible, but with the advent of digital filter it is shown to be possible.
This gave reason for people to use digital filter. As the cost was still a concern the usage was still limited to only some design.
As the VLSI developed, the cost of chips and power consumed, decreased drastically. This helped the development of digital filter design and helped it to reach common people through the household instruments.