They are cheap and easy to use. Also, you can easily create something using a micro that is the equivalent of many discrete logic chips. Given a few inexpensive software tools, a microcontroller such as the Atmel AT89C2051 should be just as easy to use as a handful of 4000-series CMOS chips. Another reason for using a micro is that micros are the future of electronics. While it is useful to know how to design with 4000-series logic, most new products require more than can be easily done in discrete logic.
Software development is now that much more convenient.
The heart of the hardware is, of course, the Atmel '2051 micro. To make it start predictably, we need a reset circuit consisting of C7. D2 forces C7 to discharge quickly when power is removed. To set how fast it thinks, we need an external crystal X1 and associated capacitors C1 and C2. Note that the specified crystal could be replaced by a ceramic resonator or crystal in the 10MHz to 12MHz range without any significant change in performance.