In some occasions yes and in others no. Since almost every mine is different from any other mine in at least one or more item, broad generalities are almost always suspect.

If the mine has easy to identify and easy to isolate bands that contribute to low quality, selective mining is quite likely your choice. A good example would be a surface mine with hard shale bands between coal layers.

If it would be very difficult to isolate them then upgrading is the choice. A good example is the same seams as in the surface mine, but being mined underground. It may now difficult to mine the coal and shale separately.

It depends on the coal-mineral association. In some instances coal processing, specifically crushing as the first stage of the process liberates value that would have otherwise been lost to selective mining. 'Better' also makes it very tricky. If I had a mining license for 3 years for a 18Mt reserve and was only able to process 3MTPA, I would selectively mine as far as I can! But it depends on the Mineral Resources Management strategy ultimately. And there is technology that can upgrade the feed stock albeit with very poor efficiencies. The jig is one that comes to mind almost immediately but the Ep values are very poor.

It is not this or that; since natural resource like coal is finite, we have to think of conservation which can be done only by washing. We may make huge profits by selective mining leaving major portion of mined product as a waste but we will be throwing huge value as waste.

For me, once you decide to mine, one should attempt to recover maximum value even if it is more expensive.Optimal recovery is a must.

Unless we know of the site/type of coal/environmental aspects etc. we will only keep on adding more and more questions.

Let an expert be engaged to get a grip on what to do and how to proceed.

As others have said, this is a very site specific question and needs to be evaluated very carefully. The selective mining of interburden material is a lot more time consuming and expensive than the initial stripping operation, so the costs/ton need to be considered. Also the equipment for hauling and disposing of the interburden waste will be very similar to the coal mining, but needs to be kept separate (probably). Off setting this is the lower need for water and wet tailings disposal.