Why Minimum circuit size problem is important?
Finding the minimum size circuit is not important in practice for large circuits. Finding small size circuits is of course important because it directly impacts the cost of building a circuit. 

Finding minimum size circuits for small circuits that are used as building blocks is quite important. For example, you'd want to know how to build the smallest possible full adder if you end up having a million of them in a processor. And you really want a minimum size circuit for a bit of memory in your L3 cache when your processor has 36MB of L3 cache or 288 million of these cells.

However, minimising the delay of a circuit is also important, and sometimes more important or even far more important than minimum size.