What are the practical uses of ASIC?
We used an ASIC in a number of products where a microcontroller used too much power. It was a fairly simple device, a couple of hundreds gates, and had to consume less than 100 nA static, which for microcontrollers at the time was not possible. Price was comparable to a microcontroller due to high quantities; you'll probably need >100 k/yr. 

An FPGA would not only have been overkill, costing a lot more, but would have needed an external code Flash, which added to the already bigger footprint.